ARITHMETIC PROPERTIES OF COLORED p-ARY PARTITIONS

被引：0

作者：

Zmija, B. ^{[1
,2
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Dept Algebra, Sokolovska 83, Prague 8, Czech Republic

[2] Jagiellonian Univ Krakow, Inst Math, Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

ACTA MATHEMATICA HUNGARICA | 2023年 / 171卷 / 1期

关键词：

p-ary partition; congruence; colored partition; generating function; CONGRUENCES;

D O I：

10.1007/s10474-023-01382-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study divisibility properties of p-ary partitions colored with k(p - 1) colors for some positive integer k. In particular, we obtain a precise description of p-adic valuations in the case of k = p(alpha) and k = p(alpha) - 1. We also prove a general result concerning the case in which finitely many parts can be colored with a number of colors smaller than k(p - 1) and all others with exactly k(p - 1) colors, where k is arbitrary (but fixed).

引用

页码：53 / 66

页数：14

共 11 条

[1]

Allouche J.-P., 2003, Automatic Sequences: Theory, Applications, Generalizations, DOI DOI 10.1017/CBO9780511546563

[2]

Andrews G.E., 1976, The Theory of Partitions

[3] CONGRUENCE PROPERTIES OF BINARY PARTITION FUNCTION [J].