Congruences on the Number of Restricted m-ary Partitions

2015/12/17 by Hou, Qing-Hu, Jin, Hai-Tao, Mu, Yan-Ping +1
#05A17 #11P83 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1512.05601

Abstract

Andrews, Brietzke, Rødseth and Sellers proved an infinite family of congruences on the number of the restricted m-ary partitions when m is a prime. In this note, we show that these congruences hold for arbitrary positive integer m and thus confirm the conjecture of Andrews, et al.

Related

• High order congruences for M-ary partitions
• On the Enumeration and Congruences for m-ary Partitions
• The distribution of the number of parts of m-ary partitions modulo m
• Recurrence sequences connected with the m--ary partition function and\n their divisibility properties
• Characterizing the number of coloured m-ary partitions modulo m, with and without gaps