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arXiv:0805.1622
From: William Y. C. Chen <chen@nankai.edu.cn>
Date: Mon, 12 May 2008 12:36:13 GMT   (11kb)

Title: Partitions of $\Integer_n$ into Arithmetic Progressions
Authors: William Y.C. Chen, David G.L. Wang, and Iris F. Zhang
Categories: math.CO
Comments: 11 pages, 2 figures
MSC-class: 05A05, 05A15
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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  We introduce the notion of arithmetic progression blocks or AP-blocks of
$\Integer_n$, which can be represented as sequences of the form $(x, x+m, x+2m,
\ldots, x+(i-1)m) \pmod n$. Then we consider the problem of partitioning
$\Integer_n$ into AP-blocks for a given difference $m$. We show that subject to
a technical condition, the number of partitions of $\Integer_n$ into
$m$-AP-blocks of a given type is independent of $m$. When we restrict our
attention to blocks of sizes one or two, we are led to a combinatorial
interpretation of a formula recently derived by Mansour and Sun as a
generalization of the Kaplansky numbers. These numbers have also occurred as
the coefficients in Waring's formula for symmetric functions.
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Contains:
 AP-s.tex: 36271 bytes

Stored as: 0805.1622.gz (11kb)

Warnings:

Author 1: William Y.C. Chen
Author 2: David G.L. Wang
Author 3: Iris F. Zhang
-> Number of authors = 3


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