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

页码：803 / 812

页数：10

共 50 条

[1] Reciprocity between partitions and compositions
George Beck
Shane Chern
The Ramanujan Journal, 2022, 59 : 803 - 812
[2] Bijections Between Colored Compositions, Dyck Paths, and Polygon Partitions
Gil, Juan B.
Hoover, Emma G.
Shearer, Jessica A.
JOURNAL OF INTEGER SEQUENCES, 2024, 27 (05)
[3] A RECIPROCITY FORMULA FOR WEIGHTED QUADRATIC PARTITIONS
CARLITZ, L
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 59 (01) : 53 - 53
[4] Partitions and compositions defined by inequalities
Corteel, S
Savage, CD
RAMANUJAN JOURNAL, 2004, 8 (03): : 357 - 381
[5] Partitions and Compositions Defined by Inequalities
Sylvie Corteel
Carla D. Savage
The Ramanujan Journal, 2004, 8 : 357 - 381
[6] COMPOSITIONS, PARTITIONS, AND FIBONACCI NUMBERS
Sills, Andrew V.
FIBONACCI QUARTERLY, 2011, 49 (04): : 348 - 354
[7] IDENTITY RELATING COMPOSITIONS AND PARTITIONS
HICKERSON, DR
FIBONACCI QUARTERLY, 1978, 16 (01): : 23 - 26
[8] On flushed partitions and concave compositions
Liu, Xiao-Chuan
EUROPEAN JOURNAL OF COMBINATORICS, 2012, 33 (04) : 663 - 678
[9] RECIPROCAL SUMS OVER PARTITIONS AND COMPOSITIONS
KNOPFMACHER, A
RIDLEY, JN
SIAM JOURNAL ON DISCRETE MATHEMATICS, 1993, 6 (03) : 388 - 399
[10] On the dimension of downsets of integer partitions and compositions
Engen, Michael
Vatter, Vincent
AUSTRALASIAN JOURNAL OF COMBINATORICS, 2019, 74 : 98 - 111

← 1 2 3 4 5 →