W.Y.C. Chen and Gian-Carlo Rota,
q-Analogs of the principle of inclusion---exclusion and permutations of restricted position,
Discrete Math. 104 (1992) 7-22.

Cited by

  1. U. Bader and U. Onn, Geometric representations of GL(n, R), cellular Hecke algebras and the embedding problem, J. Pure Appl. Algebra 208 (2007) 905-922.

  2. U. Bader and U. Onn, On some geometric representations of GLN(o), Comm. Algebra 40 (2012) 3169-3191.

  3. V. Chandrasekar and K. Suresh, Generalized q-derivative operator of the second kind and its applications, Mathematical Sciences International Research Journal 3 (2014) 214-218.

  4. V. Chandrasekar and K. Suresh, Theory and applications of generalized q-derivative operator, Int. J. Pure Appl. Math. 101 (2015) 963-973.

  5. W.Y.C. Chen, R.L. Tang and A.F.Y. Zhao, Derangement polynomials and excedances of type B, Electron. J. Combin. 16 (2009) Special volume in honor of Anders Björner, Research Paper 15, 16 pp.

  6. W.Y.C. Chen and D.H. Xu, Labeled partitions and the q-derangement numbers, SIAM J. Discrete Math. 22(3) (2008) 1099-1104.

  7. W.Y.C. Chen and E.X.W. Xia, The ratio monotonicity of the q-derangement numbers, Discrete Math. 311(6) (2011) 393-397.

  8. T. Chow, The combinatorics behind number-theoretic sieves, Adv. Math. 138 (1998) 293-305.

  9. C.-O. Chow, On derangement polynomials of type D, Taiwanese J. Math. 27(4) (2023) 629¨C646.

  10. R.J. Clarke, G.-N. Han and J. Zeng, A combinatorial interpretation of the Seidal generation of q-derangement numbers, Ann. Combin. 1 (1997) 313-327.

  11. V. Dubois, Cryptanalyse de schémas multivariés, Ph.D. Thesis, Université Paris VI, 2007.

  12. H. Feng, Structure of quasi-invariant vector spaces, J. Math. Res. Exposition 20 (2000) 197-200.

  13. H. Feng and J. Wang, Minimum cutsets for an element of a subspace lattice over a finite vector space, Order 14 (1997) 145-151.

  14. I. Gessel and C. Reutenauer, Counting permutations with given cycle structure and descent set, J. Combin. Theory Ser. A 64 (1993) 189-215.

  15. J. Haglund, q-rook polynomials and matrices over finite fields, Adv. in Appl. Math. 29 (1998) 450-487.

  16. J. Haglund, Rook theory and hypergeometric series, Adv. in Appl. Math. 17 (1996) 408-459.

  17. D.A. Klain, Kinematic formulas for finite lattices, Ann. Combin. 1 (1997) 353-366.

  18. Martin H. Krieger, Don¡¯t Just Begin with ¡°Let A be an algebra¡­¡±, Noticesofthe AMS, 65(4) (2018) 437-439.

  19. T. Kotek and J.A. Makowsky, A representation theorem for (q-)holonomic sequences, J. Comput. System Sci. 80 (2014) 363-374.

  20. J.P.S. Kung, The subset and subspace analog, In: Gian-Carlo Rota on Combinatorics, 277-282, Birkhäuser, 1995.

  21. E.H. Liu and W.J. Du, The log-concavity of the q-derangement numbers of type B, Open Math. 16 (2018) 127-132.

  22. M. Mavronicolas, A q-analog of approximate inclusion-exclusion, Adv. in Appl. Math. 20 (1998) 108-129.

  23. E. Munarini, Generalized q-Fibonacci numbers, Fibonacci Quart. 43(3) (2005) 234-242.

  24. A. Samorodnitsky, Approximate inclusion-exclusion and orthogonal polynomials, Preprint.

  25. J. Wang, Quotient sets and subset-subspace analogy, Adv. in Appl. Math. 23 (1999) 333-339.

  26. J. Wang and H.J. Zhang, q-Weighted log-concavity and q-direct product theorem on the normality of posets, Adv. in Appl. Math. 41(3) (2008) 395-406.

  27. J. Wang and H.J. Zhang, Normalized matching property of restricted subspace lattices, SIAM J. Discrete Math. 22(1) (2008) 248-255.

  28. J. Wang and H.J. Zhang, Nontrivial independent sets of bipartite graphs and cross-intersecting families, J. Combin. Theory Ser. A 120(1) (2013) 129-141.

  29. X.D. Zhang, On a kind of sequence of polynomials, In: Computing and Combinatorics, 379-383, Lecture Notes in Comput. Sci. 959, Springer, Berlin, 1995.

  30. X.D. Zhang, On the spiral property of q-derangement numbers, Discrete Math. 159 (1996) 295-298.