Arithmetic Properties of m-ary Partitions Without Gaps

George E. Andrews; Eduardo Brietzke; Øystein J. Rødseth; James Sellers

doi:10.1007/s00026-017-0369-6

Arithmetic Properties of m-ary Partitions Without Gaps

George E. Andrews, Eduardo Brietzke, Øystein J. Rødseth, James Sellers

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Motivated by recent work of Bessenrodt, Olsson, and Sellers on unique path partitions, we consider partitions of an integer n wherein the parts are all powers of a fixed integer m≥ 2 and there are no "gaps" in the parts; that is, if mⁱ is the largest part in a given partition, then m^j also appears as a part in the partition for each 0 ≤ j< i. Our ultimate goal is to prove an infinite family of congruences modulo powers of m which are satisfied by these functions.

Original language	English (US)
Pages (from-to)	495-506
Number of pages	12
Journal	Annals of Combinatorics
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/s00026-017-0369-6
State	Published - Dec 1 2017
Externally published	Yes

Keywords

congruences
m-ary partitions
unique path partitions

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10.1007/s00026-017-0369-6

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abstract = "Motivated by recent work of Bessenrodt, Olsson, and Sellers on unique path partitions, we consider partitions of an integer n wherein the parts are all powers of a fixed integer m≥ 2 and there are no {"}gaps{"} in the parts; that is, if mi is the largest part in a given partition, then mj also appears as a part in the partition for each 0 ≤ j< i. Our ultimate goal is to prove an infinite family of congruences modulo powers of m which are satisfied by these functions.",

keywords = "congruences, m-ary partitions, unique path partitions",

author = "Andrews, {George E.} and Eduardo Brietzke and R{\o}dseth, {{\O}ystein J.} and James Sellers",

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T1 - Arithmetic Properties of m-ary Partitions Without Gaps

AU - Andrews, George E.

AU - Brietzke, Eduardo

AU - Rødseth, Øystein J.

AU - Sellers, James

PY - 2017/12/1

Y1 - 2017/12/1

N2 - Motivated by recent work of Bessenrodt, Olsson, and Sellers on unique path partitions, we consider partitions of an integer n wherein the parts are all powers of a fixed integer m≥ 2 and there are no "gaps" in the parts; that is, if mi is the largest part in a given partition, then mj also appears as a part in the partition for each 0 ≤ j< i. Our ultimate goal is to prove an infinite family of congruences modulo powers of m which are satisfied by these functions.

AB - Motivated by recent work of Bessenrodt, Olsson, and Sellers on unique path partitions, we consider partitions of an integer n wherein the parts are all powers of a fixed integer m≥ 2 and there are no "gaps" in the parts; that is, if mi is the largest part in a given partition, then mj also appears as a part in the partition for each 0 ≤ j< i. Our ultimate goal is to prove an infinite family of congruences modulo powers of m which are satisfied by these functions.

KW - congruences

KW - m-ary partitions

KW - unique path partitions

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JO - Annals of Combinatorics

JF - Annals of Combinatorics

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ER -

Arithmetic Properties of m-ary Partitions Without Gaps

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