Proof of a monotonicity conjecture

Thomas Prellberg; D. Stanton

doi:10.1016/S0097-3165(03)00056-6

Proof of a monotonicity conjecture

Thomas Prellberg
, D. Stanton

School of Mathematics

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

4 Scopus citations

Abstract

If p_k(P) is the number of integer partitions of k≥1 whose parts lie in P, it is shown that p_k (P) is an increasing function of k for P = {n, n + 1, ..., 2n - 1}, where n ≥, 3 is odd. This completes the classification of all such monotonic P with min (P) ≠ 2, 3, or 5.

Original language	English (US)
Pages (from-to)	377-381
Number of pages	5
Journal	Journal of Combinatorial Theory. Series A
Volume	103
Issue number	2
DOIs	https://doi.org/10.1016/S0097-3165(03)00056-6
State	Published - Aug 2003

Bibliographical note

Funding Information:
Research partially supported by NSF Grant DMS-0203282.

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10.1016/S0097-3165(03)00056-6

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title = "Proof of a monotonicity conjecture",

abstract = "If pk(P) is the number of integer partitions of k≥1 whose parts lie in P, it is shown that pk (P) is an increasing function of k for P = \{n, n + 1, ..., 2n - 1\}, where n ≥, 3 is odd. This completes the classification of all such monotonic P with min (P) ≠ 2, 3, or 5.",

author = "Thomas Prellberg and D. Stanton",

note = "Funding Information: Research partially supported by NSF Grant DMS-0203282. ",

year = "2003",

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N2 - If pk(P) is the number of integer partitions of k≥1 whose parts lie in P, it is shown that pk (P) is an increasing function of k for P = {n, n + 1, ..., 2n - 1}, where n ≥, 3 is odd. This completes the classification of all such monotonic P with min (P) ≠ 2, 3, or 5.

AB - If pk(P) is the number of integer partitions of k≥1 whose parts lie in P, it is shown that pk (P) is an increasing function of k for P = {n, n + 1, ..., 2n - 1}, where n ≥, 3 is odd. This completes the classification of all such monotonic P with min (P) ≠ 2, 3, or 5.

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UR - https://www.scopus.com/pages/publications/0042352676#tab=citedBy

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DO - 10.1016/S0097-3165(03)00056-6

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AN - SCOPUS:0042352676

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VL - 103

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EP - 381

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

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ER -

Proof of a monotonicity conjecture

Abstract

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