Congruence Modulo 4 for Andrews' Even Parts Below Odd Parts Partition Function

被引：1

作者：

Chen, Dandan ^{[1
]}

Chen, Rong ^{[2
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai, Peoples R China

[2] Tongji Univ, Sch Math Sci, Shanghai, Peoples R China

来源：

ANNALS OF COMBINATORICS | 2023年 / 27卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Ternary quadratic form; Ramanujan-type congruences; Class number; TERNARY QUADRATIC-FORMS; INTEGER PARTITIONS; CLASS NUMBER; REPRESENTATIONS;

D O I：

10.1007/s00026-023-00645-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We find and prove a class of congruences modulo 4 for Andrews' partition with certain ternary quadratic form. We also discuss distribution of (epsilon O) over bar (n) and further prove that (epsilon O) over bar (n) = 0 (mod 4) for almost all n. This study was inspired by similar congruences modulo 4 in the work by the second author and Garvan.

引用

页码：269 / 279

页数：11

共 50 条

[41] NEW CONGRUENCES MODULO SMALL POWERS OF 2 FOR OVERPARTITIONS INTO ODD PARTS
Hemanthkumar, B.
Chandankumar, S.
MATEMATICKI VESNIK, 2021, 73 (02): : 141 - 148
[42] A conjecture of Pore and Fathima on congruences modulo 20 for Andrews' partition function
Guadalupe, Russelle
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2025, 31 (02):
[43] Congruences modulo 16, 32 and 64 for bipartitions with distinct even parts
Liu, Eric H.
Yao, Olivia X. M.
Zhao, Tao Yan
ARS COMBINATORIA, 2018, 140 : 301 - 310
[44] IDENTITIES RELATING NUMBER OF PARTITIONS INTO AN EVEN AND ODD NUMBER OF PARTS
ALDER, HL
MUWAFI, AA
FIBONACCI QUARTERLY, 1975, 13 (02): : 147 - 149
[45] SOME PROPERTIES OF INTEGRALS OF EVEN AND ODD PARTS OF HURWITZ POLYNOMIALS
VERMA, PK
RAMACHANDRAN, V
IEEE TRANSACTIONS ON CIRCUIT THEORY, 1973, CT20 (03): : 312 - 314
[46] IDENTITIES RELATING NUMBER OF PARTITIONS INTO AN EVEN AND ODD NUMBER OF PARTS
HICKERSON, DR
ALDER, HL
MUWAFI, AA
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (05): : A541 - A541
[47] COMBINATORIAL PROOF OF A THEOREM ON PARTITIONS INTO AN EVEN OR ODD NUMBER OF PARTS
GUPTA, H
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1976, 21 (01) : 100 - 103
[48] CONTINUED FRACTIONS WHOSE EVEN AND ODD PARTS CONVERGE ABSOLUTELY
LANE, RE
WALL, HS
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1949, 55 (03) : 285 - 285
[49] On partitions with fixed number of even-indexed and odd-indexed odd parts
Berkovich, Alexander
Uncu, Ali Kemal
JOURNAL OF NUMBER THEORY, 2016, 167 : 7 - 30
[50] SOME NEW INFINITE FAMILIES OF CONGRUENCES MODULO 3 FOR OVERPARTITIONS INTO ODD PARTS
Xia, Ernest X. W.
COLLOQUIUM MATHEMATICUM, 2016, 142 (02) : 255 - 266

← 1 2 3 4 5 →