INVERSIONS IN COMPOSITIONS OF INTEGERS

被引：8

作者：

Heubach, S. ^{[1
]}

Knopfmacher, A. ^{[2
]}

Mays, M. E. ^{[3
]}

Munagi, A. ^{[2
]}

机构：

[1] Calif State Univ Los Angeles, Dept Math, Los Angeles, CA 90032 USA

[2] Univ Witwatersrand, John Knopfmacher Ctr Applicable Anal & Number The, Johannesburg, South Africa

[3] W Virginia Univ, Morgantown, WV 26506 USA

来源：

QUAESTIONES MATHEMATICAE | 2011年 / 34卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Composition; inversion;

D O I：

10.2989/16073606.2011.594234

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A composition of the positive integer n is a representation of n as an ordered sum of positive integers n = a(1) + a(2) + ... + am. It is well known that there are 2(n-1) compositions of n. An inversion in a composition is a pair of summands {a(i), a(j)} for which i < j and a(i) > a(j). The number of inversions of a composition is an indication of how far the composition is from a partition of n, which by convention uses a sequence of nondecreasing summands and has no inversions. We consider counting techniques for determining both the number of inversions in the set of compositions of n and the number of compositions of n with a given number of inversions. We provide explicit bijections to resolve several conjectures, and also consider asymptotic results.

引用

页码：187 / 202

页数：16

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