Reciprocity between partitions and compositions

被引：0
|
作者：
Beck, George [1 ,2 ]
Chern, Shane [1 ]
机构：
[1] Dalhousie Univ, Dept Math & Stat, Halifax, NS B3H 4R2, Canada
[2] Wolfram Res Inc, Champaign, IL 61820 USA
来源：
RAMANUJAN JOURNAL | 2022年 / 59卷 / 03期
关键词：
Partitions; Compositions; Reciprocity;
D O I：
10.1007/s11139-021-00541-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show that both their generating functions and two matrices determined by them satisfy certain reciprocal relations.
引用
收藏
页码：803 / 812
页数：10
相关论文
共 50 条
  • [21] Shift-induced dynamical systems on partitions and compositions
    Hopkins, Brian
    Jones, Michael A.
    ELECTRONIC JOURNAL OF COMBINATORICS, 2006, 13 (01):
  • [22] COUNTING WATER CELLS IN BARGRAPHS OF COMPOSITIONS AND SET PARTITIONS
    Mansour, Toufik
    Shattuck, Mark
    APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2018, 12 (02) : 413 - 438
  • [23] Counting corners in compositions and set partitions presented as bargraphs
    Mansour, Toufik
    Shabani, Armend Sh.
    Shattuck, Mark
    JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2018, 24 (06) : 992 - 1015
  • [24] Asymptotics of the Uniform Measures on Simplices and Random Compositions and Partitions
    A. M. Vershik
    Yu. V. Yakubovich
    Functional Analysis and Its Applications, 2003, 37 : 273 - 280
  • [25] Asymptotics of the uniform measures on simplices and random compositions and partitions
    Vershik, AM
    Yakubovich, YV
    FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2003, 37 (04) : 273 - 280
  • [26] A Bijection between Atomic Partitions and Unsplitable Partitions
    Chen, William Y. C.
    Li, Teresa X. S.
    Wang, David G. L.
    ELECTRONIC JOURNAL OF COMBINATORICS, 2011, 18 (01):
  • [27] About the dynamics of some systems based on integer partitions and compositions
    Goles, E
    Morvan, M
    Phan, HD
    FORMAL POWER SERIES AND ALGEBRAIC COMBINATORICS, 2000, : 214 - 225
  • [28] On the coincidence of limit shapes for integer partitions and compositions, and a slicing of young diagrams
    Yakubovich Yu.V.
    Journal of Mathematical Sciences, 2005, 131 (2) : 5569 - 5577
  • [29] Compositions of n as alternating sequences of weakly increasing and strictly decreasing partitions
    Blecher, Aubrey
    Brennan, Charlotte
    Mansour, Toufik
    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2012, 10 (02): : 788 - 796
  • [30] Transfer distance between partitions
    Denoeud, Lucile
    ADVANCES IN DATA ANALYSIS AND CLASSIFICATION, 2008, 2 (03) : 279 - 294
12345