A note on the parity of broken 7-diamond partitions

被引：1

作者：

Dai, Haobo ^{[1
]}

机构：

[1] Anhui Univ Sci & Technol, Sch Sci, Middle Shungeng Rd 168, Huainan 232001, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2016年 / 12卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Broken 7-diamond partition; binary quadratic forms; modular forms; congruence; K-DIAMOND PARTITIONS; 3-DIAMOND PARTITIONS; ETA-QUOTIENTS; CONGRUENCES; ANDREWS; FORMS;

D O I：

10.1142/S1793042116501025

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we find many new parity results for broken 7-diamond partitions by using a result of Berkovich and Patane. For example, we prove that Delta(7) (8.2(6 alpha) n + 8.2(6 alpha-1) + 2/3) equivalent to 0 (mod 2), for all n >= 0 and alpha >= 1.

引用

页码：1669 / 1674

页数：6

共 50 条

[31] A Note on Andrews' Partitions with Parts Separated by Parity
Bringmann, Kathrin
Jennings-Shaffer, Chris
ANNALS OF COMBINATORICS, 2019, 23 (3-4) : 573 - 578
[32] A Note on Andrews’ Partitions with Parts Separated by Parity
Kathrin Bringmann
Chris Jennings-Shaffer
Annals of Combinatorics, 2019, 23 : 573 - 578
[33] New Congruences for Broken k-Diamond Partitions
Tang, Dazhao
JOURNAL OF INTEGER SEQUENCES, 2018, 21 (05)
[34] New Congruences for Broken k-Diamond and k Dots Bracelet Partitions
Yu, Jing-Jun
MATHEMATICAL NOTES, 2022, 112 (3-4) : 393 - 405
[35] Newman’s identity and infinite families of congruences modulo 7 for broken 3-diamond partitions
Olivia X. M. Yao
Ya Juan Wang
The Ramanujan Journal, 2017, 43 : 619 - 631
[36] Congruences modulo 4 for broken k-diamond partitions
Ernest X. W. Xia
The Ramanujan Journal, 2018, 45 : 331 - 348
[37] Congruences modulo 11 for broken 5-diamond partitions
Eric H. Liu
James A. Sellers
Ernest X. W. Xia
The Ramanujan Journal, 2018, 46 : 151 - 159
[38] Parity results for 7-regular and 23-regular partitions
Baruah, Nayandeep Deka
Das, Kuwali
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2015, 11 (07) : 2221 - 2238
[39] Partitions weighted by the parity of the crank
Choi, Dohoon
Kang, Soon-Yi
Lovejoy, Jeremy
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2009, 116 (05) : 1034 - 1046
[40] Elementary proofs of Radu and Sellers’ results for broken 2-diamond partitions
Bernard L. S. Lin
Andrew Y. Z. Wang
The Ramanujan Journal, 2015, 37 : 291 - 297

← 1 2 3 4 5 →