Combinatorics of integer partitions with prescribed perimeter

被引：2

作者：

Lin, Zhicong ^{[1
]}

Xiong, Huan ^{[2
]}

Yan, Sherry H. F. ^{[3
]}

机构：

[1] Shandong Univ, Res Ctr Math & Interdisciplinary Sci, Qingdao 266237, Peoples R China

[2] Harbin Inst Technol, Inst Adv Study Math, Harbin 150001, Peoples R China

[3] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2023年 / 197卷

基金：

美国国家科学基金会;

关键词：

Integer partition; Perimeter; Repeated part; Even part; Euler's partition theorem;

D O I：

10.1016/j.jcta.2023.105747

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the number of even parts and the number of times that parts are repeated have the same distribution over integer partitions with a fixed perimeter. This refines Straub's analog of Euler's Odd-Distinct partition theorem. We generalize the two concerned statistics to those of the part-difference less than d and the parts not congruent to 1 modulo d + 1 and prove a distribution inequality, that has a similar flavor as Alder's ex-conjecture, over partitions with a prescribed perimeter. Both of our results are proven analytically and combinatorially.& COPY; 2023 Elsevier Inc. All rights reserved.

引用

页数：19