Congruence Properties of Binary Partition Functions

Katherine Anders; Melissa Dennison; Jennifer Weber Lansing; Bruce Reznick

doi:10.1007/s00026-013-0188-3

Congruence Properties of Binary Partition Functions

Katherine Anders, Melissa Dennison, Jennifer Weber Lansing, Bruce Reznick

Mathematics

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

Abstract

Let A be a finite subset of N containing 0, and let f (n) denote the number of ways to write n in the form ∑ε_j2^j, where ε_j∈A. We show that there exists a computable T = T(A) so that the sequence (f (n) mod 2) is periodic with period T. Variations and generalizations of this problem are also discussed.

Original language	English (US)
Pages (from-to)	15-26
Number of pages	12
Journal	Annals of Combinatorics
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/s00026-013-0188-3
State	Published - Mar 2013

Keywords

Stern sequence
digital representations
partitions

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Online availability

10.1007/s00026-013-0188-3

Library availability

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title = "Congruence Properties of Binary Partition Functions",

abstract = "Let A be a finite subset of N containing 0, and let f (n) denote the number of ways to write n in the form ∑εj2j, where εj∈A. We show that there exists a computable T = T(A) so that the sequence (f (n) mod 2) is periodic with period T. Variations and generalizations of this problem are also discussed.",

keywords = "Stern sequence, digital representations, partitions",

author = "Katherine Anders and Melissa Dennison and Lansing, {Jennifer Weber} and Bruce Reznick",

note = "Funding Information: ∗Anders and Lansing received support from National Science Foundation grant DMS 0838434 EMSW21MCTP: Research Experience for Graduate Students.",

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T1 - Congruence Properties of Binary Partition Functions

AU - Anders, Katherine

AU - Dennison, Melissa

AU - Lansing, Jennifer Weber

AU - Reznick, Bruce

N1 - Funding Information: ∗Anders and Lansing received support from National Science Foundation grant DMS 0838434 EMSW21MCTP: Research Experience for Graduate Students.

PY - 2013/3

Y1 - 2013/3

N2 - Let A be a finite subset of N containing 0, and let f (n) denote the number of ways to write n in the form ∑εj2j, where εj∈A. We show that there exists a computable T = T(A) so that the sequence (f (n) mod 2) is periodic with period T. Variations and generalizations of this problem are also discussed.

AB - Let A be a finite subset of N containing 0, and let f (n) denote the number of ways to write n in the form ∑εj2j, where εj∈A. We show that there exists a computable T = T(A) so that the sequence (f (n) mod 2) is periodic with period T. Variations and generalizations of this problem are also discussed.

KW - Stern sequence

KW - digital representations

KW - partitions

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JF - Annals of Combinatorics

IS - 1

ER -

Congruence Properties of Binary Partition Functions

Abstract

Keywords

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