W.Y.C. Chen, E.Y.P. Deng, R.R.X. Du, R.P. Stanley and C.H. Yan,
Crossings and nestings of matchings and partitions,
Trans. Amer. Math. Soc. 359(4) (2007) 1555-1575.

Cited by

1. H. Acan, On a uniformly random chord diagram and its intersection graph, Discrete Math. 340 (2017) 1967-1985.

2. H. Acan and B. Pittel, Formation of a giant component in the intersection graph of a random chord diagram, J. Combin. Theory Ser. B 125 (2017) 33-79.

3. N. Anderson, M. Breunig, K. Goryl, H. Lewis, M. Riehl and M. Scanlan, Properties of RNA secondary structure matching models, Involve 12 (2019) 257-280.

4. D. Armstrong, Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups, Amer. Math. Soc. 2009.

5. D. Armstrong, C. Stump and H. Thomas, A uniform bijection between nonnesting and noncrossing partitions, Trans. Amer. Math. Soc. 365 (2013) 4121-4151.

6. J. Baik and R. Jenkins, Limiting distribution of maximal crossing and nesting of Poissonized random matchings, Ann. Probab. 41 (2013) 4359-4406.

7. J. Baik and Z.P. Liu, Discrete Toeplitz/Hankel determinants and the width of nonintersecting processes, Int. Math. Res. Not. IMRN (2014) 5737-5768.

8. R. Ben-Ari, Combinatorial parameters on matchings in complete and complete bipartite graphs, Master Thesis, Bar-Ilan University, 2010.

9. G. Benkart and T. Halverson, Partition algebras and the invariant theory of the symmetric group, arXiv:1709.07751.

10. G. Benkart, T. Halverson and N. Harman, Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups, J. Algebraic Combin. 46 (2017) 77-108.

11. B. Bényi, Inversions in 312-permutations, Creat. Math. Inform. 23 (2014) 147-152.

12. B. Bényi, Advances in bijective combinatorics, Ph.D. Thesis, Bolyai Institute, 2014.

13. O. Bernardi, M. Bousquet-Mélou and K. Raschel, Counting quadrant walks via Tutte's invariant method, arXiv:1708.08215.

14. N. Blitvić, The (q, t)-Gaussian process, J. Funct. Anal. 263 (2012) 3270-3305.

15. N. Blitvić, Two-parameter non-commutative central limit theorem, Probabilités et Statistiques. 50 (2014) 1456-1473.

16. J. Bloom, Pattern avoiding permutations & rook placements, Ph.D. Thesis, Dartmouth College, 2014.

17. J. Bloom and S. Elizalde, Pattern avoidance in matchings and partitions, Electron. J. Combin. 20 (2013) Paper 5, 38 pp.

18. J. Bloom and S. Elizalde, Patterns in matchings and rook placements, Discrete Math. Theor. Comput. Sci. (2013) 909-920.

19. J. Bloom and D. Saracino, Pattern avoidance for set partitionsà la Klazar, Discrete Math. Theor. Comput. Sci. 18 (2016) Paper No. 9, 22 pp.

20. M. Bousquet-Mélou, A. Claesson, M. Dukes and and S. Kitaev, Unlabeled (2+ 2)-free posets, ascent sequences and pattern avoiding permutations, DMTCS proc. AK (2009) 216-228.

21. M. Bousquet-Mélou, A. Claesson, M. Dukes and S. Kitaev, (2+ 2)-free posets, ascent sequences and pattern avoiding permutations, J. Combin. Theory Ser. A 117 (2010) 884-909.

22. M. Bousquet-Mélou and G.C. Xin, On partitions avoiding 3-crossings, Sém. Lothar. Combin. 54 (2005/07) Art. B54e, 21 pp.

23. S. Burrill, Crossings and nestings in four combinatorial families, Master Thesis, Simon Fraser University, 2009.

24. S. Burrill, J. Courtiel, E. Fusy, S. Melczer and M. Mishna, Tableau sequences, open diagrams, and Baxter families, European J. Combin. 58 (2016)144-165.

25. S. Burrill, S. Elizalde, M. Mishna and L. Yen, Generating trees for partitions and permutations with no k-nestings, DMTCS proc. AR (2012) 409-420.

26. S. Burrill, S. Elizalde, M. Mishna and L. Yen, A generating tree approach to k-nonnesting partitions and permutations, Ann. Comb. 20 (2016) 453-485.

27. S. Burrill, S. Melczer and M. Mishna, A baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape, In: Proceedings of FPSAC 2015, 369-380, Discrete Math. Theor. Comput. Sci. Proc., Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2015.

28. S. Burrill, M. Mishna and J. Post, On k-crossings and k-nestings of permutations, In: 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 593-600, Discrete Math. Theor. Comput. Sci. Proc., AN, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2010.

29. S. Burrill and L. Yen, Constructing skolem sequences via generating trees, arXiv:1301.6424.

30. Y. Cai, New perspectives of quantum analogues, Ph.D. Thesis, University of Kentucky, 2016.

31. J.H.C. Chan, An infinite family of inv-Wilf-equivalent permutation pairs, European J. Combin. 44 (2015) 57-76.

32. J.H.C. Chan, Three problems involving permutations, Ph.D. Thesis, Simon Fraser University, 2016.

33. W. Chen, Enumeration of set partitions refined by crossing and nesting numbers, Master Thesis, Rutgers University, 2010.

34. W.Y.C. Chen, Log-concavity and q-log-convexity conjectures on the longest increasing subsequences of permutations, arXiv:0806.3392.

35. W.Y.C. Chen, N.J.Y. Fan and A.F.Y. Zhao, Partitions and partial matchings avoiding neighbor patterns, European J. Combin. 33 (2012) 491-504.

36. W.Y.C. Chen, I.M. Gessel, C.H. Yan and A.L.B Yang, A major index for matchings and set partitions, J. Combin. Theory Ser. A 115 (2008) 1069-1076.

37. W.Y.C. Chen and P.L. Guo, Oscillating rim hook tableaux and colored matchings, Adv. Appl. Math. 48 (2012) 393-406.

38. W.Y.C. Chen, P.L. Guo and S.X.M. Pang, Vacillating hecke tableaux and linked partitions, Math. Z. 281 (2015) 661-672.

39. W.Y.C. Chen, Q.-H. Guo, L.H. Sun and J. Wang, Zigzag stacks and m-regular linear stacks. J. Comput. Biol. 21 (2014) 915-935.

40. W.Y.C. Chen, H.S.W. Han and C.M. Reidys, Random k-noncrossing RNA structures, Proc. Natl. Acad. Sci. 106 (2009) 22061-22066.

41. W.Y.C. Chen, T. Mansour and S.H.F. Yan, Matchings avoiding partial patterns, Electron. J. Combin. 13 (2006) Research Paper 112, 17 pp.

42. W.Y. C. Chen, S.X.M. Pang, E.X.Y. Qu and R. Stanley, Pairs of noncrossing free Dyck paths and noncrossing partitions, Discrete Math. 309 (2009) 2834-2838.

43. W.Y.C. Chen, S. Poznanovic, C.H. Yan and A.L.B. Yang, Major index for 01-fillings of moon polyominoes, J. Combin. Theory Ser. A 117 (2010) 1058-1081.

44. W.Y.C. Chen, J. Qin and C.M. Reidys, Crossings and nestings in tangled diagrams. Electron. J. Combin. 15 (2008) Research Paper 86, 14 pp.

45. W.Y.C. Chen, J. Qin and C.M. Reidys, Efficient counting and asymptotics of k-noncrossing tangled diagrams, Electron. J. Combin. 16 (2009) Research Paper 37, 8 pp.

46. W.Y.C. Chen, A.Y.Z. Wang, C.H. Yan and Alina F.Y. Zhao, Mixed statistics on 01-fillings of moon polyominoes, SIAM J. Discrete Math. 24 (2010) 1272-1290.

47. W.Y.C. Chen, S.Y.J. Wu and C.H. Yan, Linked partitions and linked cycles, European J. Combin. 29 (2008) 1408-1426.

48. B. Chern, P. Diaconis, D.M. Kane and R.C. Rhoades, Closed expressions for averages of set partition statistics, Res. Math. Sci. 1 (2014) Art. 2, 32 pp.

49. B. Chern, P. Diaconis, D.M. Kane and R.C. Rhoades, Central limit theorems for some set partition statistics, Adv. in Appl. Math. 70 (2015) 92-105.

50. J.K.H. Chiu and Y.P.P. Chen, Conformational features of topologically classified RNA secondary structures, PloS one 7 (2012) e39907.

51. A. Conflitti and R. Mamede, On noncrossing and nonnesting partitions of type D, Ann. Comb. 15 (2011) 637-654.

52. S. Corteel, Crossings and alignments of permutations, Adv. in Appl. Math. 38 (2007) 149-163.

53. J. Courtiel, É. Fusy, M. Lepoutre and M. Mishna, Bijections for walks ending on an axis, using open arc diagrams, Electronic Notes in Discrete Mathematics 61 (2017) 301-307.

54. J. Courtiel, É. Fusy, M. Lepoutre and M. Mishna, Bijections for Weyl chamber walks ending on an axis, using arc diagrams and Schnyder woods, European J. Combin. 69 (2018) 126-142.

55. A. de Mier, On the symmetry of the distribution of k-crossings and k-nestings, Electron. J. Combin. 13 (2006) Note 21, 6 pp.

56. A. de Mier, k-noncrossing and k-nonnesting graphs and fillings of Ferrers diagrams, Combinatorica 27 (2007) 699-720.

57. P. Diaconis and R. Graham, The magic of Charles Sanders Peirce, Preprint.

58. C.-P. Dong, Folded bump diagrams for partitions of classical types, Adv. in Appl. Math. 62 (2015) 141-159.

59. T. Doslić and D. Veljan, Secondary structures, plane trees and motzkin numbers, Math. Commun. 12 (2007) 163-169.

60. D. Drake, The combinatorics of associated hermite polynomials, European J. Combin. 30 (2009) 1005-1021.

61. D. Drake, Bijections from weighted dyck paths to Schröeder paths, J. Integer Seq. 13 (2010) Article 10.9.2, 20 pp.

62. D. Drake and J.S. Kim, k-distant crossings and nestings of matchings and partitions, arXiv:0812.2725.

63. S. Elizalde, A bijection between 2-triangulations and pairs of non-crossing Dyck paths, J. Combin. Theory Ser. A 114 (2007)1481-1503.

64. S.-P. Eu, T.-S. Fu, J.T. Hou and T.-W. Hsu, Standard Young tableaux and colored Motzkin paths, J. Combin. Theory Ser. A 120 (2013) 1786-1803.

65. V. Féray, Weighted dependency graphs, Electron. J. Probab. 23 (2018) 1-65.

66. G. Fertin, D. Hermelin, R. Rizzi and S. Vialette, Finding common structured patterns in linear graphs, Theoret. Comput. Sci. 411 (2010) 2475-2486.

67. J.B. Gil, P.R.W. McNamara, J.O. Tirrell and M.D. Weiner, From Dyck paths to standard Young tableaux, arXiv:1708.00513.

68. A.M. Goyt, Avoidance of partitions of a three-element set, Adv. in Appl. Math. 41 (2008) 95-114.

69. Q.-H. Guo, L.H. Sun and J. Wang, Regular simple queues of protein contact maps, Bull. Math. Biol. 79 (2017) 21-35.

70. T. Halverson and E. delMas, Representations of the rook-Brauer algebra, Comm. Algebra 42 (2014) 423-443.

71. T. Halverson and T. Lewandowski, RSK insertion for set partitions and diagram algebras, Electron. J. Combin. 11 (2004/06) Research Paper 24, 24 pp.

72. T. Halverson and N. Thiem, q-Partition algebra combinatorics, J. Combin. Theory Ser. A 117 (2010) 507-527.

73. A. Hamdi, Symmetric distribution of crossings and nestings in permutations of type B, Electron. J. Combin. 18 (2011) Paper 200, 9 pp.

74. G.-N. Han and H. Xiong, Polynomiality of certain average weights for oscillating tableaux, arXiv:1709.00635.

75. H.S.W. Han and C.M. Reidys, Pseudoknot RNA structures with arc-length $\geq$ 4, J. Comput. Biol. 15 (2008) 1195-1208.

76. H.S.W. Han and C.M. Reidys, Stacks in canonical RNA pseudoknot structures, Math. Biosci. 219 (2009) 7-14.

77. H.S.W. Han and C.M. Reidys, The 5'-3' distance of RNA secondary structures, J. Comput. Biol. 19 (2012) 867-878.

78. S. Heubach and T. Mansour, Combinatorics of Compositions and Words, CRC Press, 2009.

79. S. Hopkins and I. Zhang, A note on statistical averages for oscillating tableaux, Electron. J. Combin. 22 (2015) Paper 2.48, 9 pp.

80. F.W.D. Huang, L.Y.M. Li and C.M. Reidys, Sequence-structure relations of pseudoknot RNA, BMC bioinformatics 10 (2009) 1, 19 pp.

81. F.W.D. Huang, M.E. Nebel and C.M. Reidys, Generation of RNA pseudoknot structures with topological genus filtration, Math. Biosci. 245 (2013) 216-225.

82. F.W.D. Huang, W.W.J. Peng and C.M. Reidys, Folding 3-noncrossing RNA pseudoknot structures, J. Comput. Biol. 16 (2009) 1549-1575.

83. F.W.D. Huang and C.M. Reidys, Statistics of canonical RNA pseudoknot structures, J. Theoret. Biol. 253 (2008) 570-578.

84. F.W.D. Huang and C.M. Reidys, On the uniform generation of modular diagrams, Electron. J. Combin. 17 (2010) Research paper 175, 16 pp.

85. A.F. Jefferson, The substitution decomposition of matchings and RNA secondary structures, Ph.D. Thesis, University of Florida, 2015.

86. V. Jelínek, Dyck paths and pattern-avoiding matchings, European J. Combin. 28 (2007) 202-213.

87. V. Jelínek, N.Y. Li, T. Mansour and S.H.F. Yan, Matchings avoiding partial patterns and lattice paths, Electron. J. Combin. 13 (2006) Research Paper 89, 12 pp.

88. V. Jelínek and T. Mansour, On pattern-avoiding partitions, Electron. J. Combin. 15 (2008) Research paper 39, 52 pp.

89. V. Jelínek and T. Mansour, Matchings and partial patterns, Electron. J. Combin. 17 (2010) Research Paper 158, 30 pp.

90. V. Jelínek, T. Mansour and M. Shattuck, On multiple pattern avoiding set partitions, Adv. in Appl. Math. 50 (2013) 292-326.

91. E.Y. Jin, J. Qin and C.M. Reidys, On k-noncrossing partitions, arXiv:0710.5014.

92. E.Y. Jin, J. Qin and C.M. Reidys, Combinatorics of RNA structures with pseudoknots, Bull. Math. Biol. 70 (2008) 45-67.

93. E.Y. Jin and C.M. Reidys, Pseudoknot RNA structures with arc-length $\geq$3, arXiv:0708.3134.

94. E.Y. Jin and C.M. Reidys, Central and local limit theorems for RNA structures, J. Theoret. Biol. 250 (2008) 547-559.

95. E.Y. Jin and C.M. Reidys, Asymptotic enumeration of RNA structures with pseudoknots, Bull. Math. Biol. 70 (2008) 951-970.

96. E.Y. Jin and C.M. Reidys, Combinatorial design of pseudoknot RNA, Adv. in Appl. Math. 42 (2009) 135-151.

97. E.Y. Jin and C.M. Reidys, On the decomposition of k-noncrossing RNA structures, Adv. in Appl. Math. 44 (2010) 53-70.

98. E.Y. Jin and C.M. Reidys, RNA pseudoknot structures with arc-length ≥ 3 and stack-length ≥ σ, Discrete Appl. Math. 158 (2010) 25-36.

99. E.Y. Jin, C.M. Reidys and R.R. Wang, Asymptotic analysis of k-noncrossing matchings, arXiv:0803.0848.

100. M. Josuat-Vergès, Stammering tableaux, Discrete Math. Theor. Comput. Sci. 19 (2017) Paper No. 3, 22 pp.

101. A. Kasraoui, Increasing and decreasing sequences of length two in 01-fillings of moon polyominoes, arXiv:0812.0799.

102. A. Kasraoui, d-Regular set partitions and rook placements, Séminaire Lotharingien de Combinatoire 62 (2009) Article B62a.

103. A. Kasraoui, Études combinatoires sur les permutations et partitions d'ensemble, Ph.D. Thesis, l'Université Claude Bernard-lyon 1, 2009.

104. A. Kasraoui, Ascents and descents in 01-fillings of moon polyominoes, European J. Combin. 31 (2010) 87-105.

105. A. Kasraoui, Average values of some Z-parameters in a random set partition, Electron. J. Combin. 18 (2011) Paper 228, 42 pp.

106. A. Kasraoui and J. Zeng, Distribution of crossings, nestings and alignments of two edges in matchings and partitions, Electron. J. Combin. 13 (2006) Research Paper 33, 12 pp.

107. K.S. Kedlaya and A.V. Sutherland, Hyperelliptic curves, L-polynomials, and random matrices, In: Arithmetic, geometry, cryptography and coding theory, 119-162, Contemp. Math., 487, Amer. Math. Soc., Providence, RI, 2009.

108. G.B. Kim, Distribution of descents in matchings, arXiv:1710.03896.

109. J.S. Kim, Bijections on two variations of noncrossing partitions, Discrete Math. 311 (2011) 1057-1063.

110. J.S. Kim, Front representation of set partitions, SIAM J. Discrete Math. 25 (2011) 447-461.

111. M. Kiwi and M. Loebl, Towards the distribution of the size of a largest planar matching and largest planar subgraph in random bipartite graphs, Electron. J. Combin. 15 (2008) Research Paper 135, 20 pp.

112. M. Klazar, On identities concerning the numbers of crossings and nestings of two edges in matchings, SIAM J. Discrete Math. 20 (2006) 960-976.

113. M. Klazar and M. Loebl, Enumeration workshop, Preprint.

114. M. Klazar and A. Marcus, Extensions of the linear bound in the Füredi–Hajnal conjecture, Adv. in Appl. Math. 38 (2007) 258-266.

115. C. Krattenthaler, Growth diagrams, and increasing and decreasing chains in fillings of Ferrers shapes, Adv. in Appl. Math. 37 (2006) 404-431.

116. C. Krattenthaler, Bijections between oscillating tableaux and (semi) standard tableaux via growth diagrams, J. Combin. Theory Ser. A 144 (2016) 277-291.

117. Z.C. Lin, Restricted inversion sequences and enhanced 3-noncrossing partitions, European J. Combin. 70 (2018) 202-211.

118. C.L. Liu and B.D. Li, Bicoloured ordered trees, non-nesting partitions and non-crossing partitions, Ars Combin. 124 (2016) 401-408.

119. Z. Liu, Discrete Toeplitz determinants and their applications, Ph.D. Thesis, University of Michigan, 2014.

120. W.J. Lloyd, Autonomous management of cost, performance, and resource uncertainty for migration of applications to infrastructure-as-a-service (IaaS) clouds, Ph.D. Thesis, Colorado State University, 2014.

121. W. Lloyd, S. Pallickara, O. David, J. Lyon,D.C. Sci, C.S. Univ, F. Collins and C. USA, Performance modeling to support multi-tier application deployment to infrastructure-as-a-service clouds, In: Proceedings of the 2012 IEEE/ACM Fifth International Conference on Utility and Cloud Computing, UCC¡¯12, 73-80, 2012.

122. G. Ma and C.M. Reidys, Canonical RNA pseudoknot structures, J. Comput. Biol. 15 (2008) 1257-1273.

123. T. Mansour and N. Mbarieky, Partitions of a set satisfying certain set of conditions, Discrete Math. 309 (2009) 4481-4488.

124. T. Mansour, M. Schork and M. Shattuck, Catalan numbers and pattern restricted set partitions, Discrete Math. 312 (2012) 2979-2991.

125. T. Mansour and S. Severini, Enumeration of (k, 2)-noncrossing partitions, Discrete Math. 308 (2008) 4570-4577.

126. T. Mansour and M. Shattuck, Counting peaks and valleys in a partition of a set, J. Integer Seq. 13 (2010) Article 10.6.8, 16 pp.

127. T. Mansour and M. Shattuck, Counting subwords in a partition of a set, Electron. J. Combin. 17 (2010) Research Paper 19, 21 pp.

128. T. Mansour and M. Shattuck, Partial matchings and pattern avoidance, Appl. Anal. Discrete Math. 7 (2013) 25-50.

129. T. Mansour and M. Shattuck, Some enumerative results related to ascent sequences, Discrete Math. 315 (2014) 29-41.

130. E. Marberg, Combinatorial methods of character enumeration for the unitriangular group, J. Algebra 345 (2011) 295-323.

131. E. Marberg, Crossings and nestings in colored set partitions, Electron. J. Combin. 20 (2013) Paper 6, 30 pp.

132. A.W. Marcus, New combinatorial techniques for nonlinear orders, Ph.D. Thesis, Georgia Institute of Technology, 2008.

133. R.J. Marsh and P. Martin, Tiling bijections between paths and Brauer diagrams, J. Algebr. Combin. 33 (2011) 427-453.

134. P.L. Méliot, Partitions aléatoires et théorie asymptotique des groupes symétriques, des algèbres d'Hecke et des groupes de Chevalley finis, Ph.D. Thesis, Université Paris-Est, 2010.

135. M. Mishna, On standard Young tableaux of bounded height, arXiv:1805.08130.

136. M. Mishna and L. Yen, Set partitions with no m-nesting, In: Advances in Combinatorics, 249-258, Springer, Heidelberg, 2013.

137. G. Muniasamy, A study on coloured partition algebras, Ph.D. Thesis, Pondicherry University, 2015.

138. M.E. Nebel, C.M. Reidys and R.R. Wang, Loops in canonical RNA pseudoknot structures, J. Comput. Biol. 18 (2011) 1793-1806.

139. R. Parviainen, Some bijections on set partitions, arXiv:0710.1132.

140. M.A. Phillipson, Monotone sequences in combinatorial structures, Ph.D. Thesis, Texas A&M University, 2015.

141. M. Phillipson, C.H. Yan and J. Yeh, Chains of length 2 in fillings of layer polyominoes, Electron. J. Combin. 20 (2013) Paper 51, 14 pp.

142. V. Pilaud, Multitriangulations, pseudotriangulations et quelques problèmes de réalisation de polytopes, Ph.D. Thesis, Université Paris Diderot, Universidad de Cantabria, 2010.

143. V. Pilaud and J. Rué, Analytic combinatorics of chord and hyperchord diagrams with k crossings, Adv. in Appl. Math. 57 (2014) 60-100.

144. J. Post, Combinatorics of arc diagrams, Ferrers fillings, Young tableaux and lattice paths, Master Thesis, Simon Fraserf University, 2009.

145. S. Poznanović and C.H. Yan, Maximal increasing sequences in fillings of almost-moon polyominoes, Adv. in Appl. Math. 66 (2015) 1-21.

146. S. Poznanović and C. Yan, Crossings and nestings of two edges in set partitions, SIAM J. Discrete Math. 23 (2009) 787-804.

147. S. Poznanovikj, Research on combinatorial statistics: crossings and nestings in discrete structures, Ph.D. Thesis, Texas A&M University, 2010.

148. P. Pylyavskyy, Non-crossing tableaux, Ann. Comb. 13 (2009) 323-339.

149. J. Qin and C.M. Reidys, A combinatorial framework for RNA tertiary interaction, arXiv:0710.3523.

150. J. Qin and C.M. Reidys, Random 3-noncrossing partitions, arXiv:0910.2608.

151. J. Qin and C.M. Reidys, Random k-noncrossing partitions, arXiv:0911.2960.

152. K. Raschel, Counting walks in a quadrant: a unified approach via boundary value problems, J. Eur. Math. Soc. (JEMS) 14 (2012) 749-777.

153. C.M. Reidys, Combinatorial Computational Biology of RNA: Pseudoknots and Neutral Networks, Springer, 2011.

154. C.M. Reidys and Rita R. Wang, Shapes of RNA pseudoknot structures, J. Comput. Biol. 17 (2010) 1575-1590.

155. C.M. Reidys, Rita R. Wang and Albus Y.Y. Zhao, Modular, k-noncrossing diagrams, Electron. J. Combin. 17 (2010) Research Paper 76, 37 pp.

156. M. Rubey, Increasing and decreasing sequences in fillings of moon polyominoes, Adv. in Appl. Math. 47 (2011) 57-87.

157. M. Rubey, B.E. Sagan and B.W. Westbury, Descent sets for symplectic groups, J. Algebraic Combin. 40 (2014) 187-208.

158. M. Rubey and C. Stump, Crossings and nestings in set partitions of classical types, Electron. J. Combin. 17 (2010) Research Paper 120, 19 pp.

159. R.P. Stanley, Increasing and decreasing subsequences and their variants, Proceedings of the International Congress of Mathematicians 1 (2007) 545-579.

160. R.P. Stanley, Permutations, Unpublished notes for 2010 AMS Colloquium Lectures.

161. X.-T. Su, Enumerating closed flows on forks, Discrete Math. 340 (2017) 3002-3010.

162. J.O. Tirrell, Orthogonal polynomials, lattice paths, and skew Young tableaux, Ph.D. Thesis, Brandeis University, 2016.

163. A.Y.Z. Wang and C.H. Yan, Positive and negative chains in charged moon polyominoes, Adv. in Appl. Math. 51 (2013) 467-482.

164. W.M. Weng and B.L. Liu, Noncrossing matchings with fixed points, Ars Combin. 109 (2013) 161-170.

165. G.C. Xin, Determinant formulas relating to tableaux of bounded height, Adv. in Appl. Math. 45 (2010) 197-211.

166. G.C. Xin and T.Y.J. Zhang, Enumeration of bilaterally symmetric 3-noncrossing partitions, Discrete Math. 309 (2009) 2497-2509.

167. S.H.F. Yan, Ascent sequences and 3-nonnesting set partitions, European J. Combin. 39 (2014) 80-94.

168. S.H.F. Yan, Bijections for inversion sequences, ascent sequences and 3-nonnesting set partitions, Appl. Math. Comput. 325 (2018) 24-30.

169. L. Yen, A bijection for crossings and nestings, arXiv:1209.3082.

170. L. Yen, Crossings and nestings for arc-coloured permutations and automation, Electron. J. Combin. 22 (2015) Paper 1.14, 21 pp.

171. M. Yip, Genus one partitions, Master Thesis, University of Waterloo, 2006.

172. I. Zhang, Homomesy of alignments in perfect matchings, Massachusetts Institute of Technology, 2014.

173. Âí¿¡, Ò¶ÓÀÄÏ, À×ºé´¨, ¾ùÔÈ»®·Ö, ÖÐ¹ú¿ÆÑ§: ÊýÑ§ 45 (2015) 1389-1402.