Binary partitions revisited

Øystein J. Rødseth; James A. Sellers

doi:10.1006/jcta.2001.3223

Binary partitions revisited

Øystein J. Rødseth, James A. Sellers

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Abstract

The restricted binary partition function b_k(n) enumerates the number of ways to represent n as n = 2^a0 + 2^a1 + ⋯ + 2^aj with 0 ≤ a₀ ≤ a₁ ≤ ⋯ ≤ a_j < k. We study the question of how large a power of 2 divides the difference b_k(2^r+2n)-b_k-2(2^rn) for fixed k ≥ 3, r ≥ 1, and all n ≥ 1.

Original language	English (US)
Pages (from-to)	33-45
Number of pages	13
Journal	Journal of Combinatorial Theory. Series A
Volume	98
Issue number	1
DOIs	https://doi.org/10.1006/jcta.2001.3223
State	Published - 2002
Externally published	Yes

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10.1006/jcta.2001.3223

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title = "Binary partitions revisited",

abstract = "The restricted binary partition function bk(n) enumerates the number of ways to represent n as n = 2a0 + 2a1 + ⋯ + 2aj with 0 ≤ a0 ≤ a1 ≤ ⋯ ≤ aj < k. We study the question of how large a power of 2 divides the difference bk(2r+2n)-bk-2(2rn) for fixed k ≥ 3, r ≥ 1, and all n ≥ 1.",

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AB - The restricted binary partition function bk(n) enumerates the number of ways to represent n as n = 2a0 + 2a1 + ⋯ + 2aj with 0 ≤ a0 ≤ a1 ≤ ⋯ ≤ aj < k. We study the question of how large a power of 2 divides the difference bk(2r+2n)-bk-2(2rn) for fixed k ≥ 3, r ≥ 1, and all n ≥ 1.

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Binary partitions revisited

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