On the largest size of (t, t + 1, ..., t + p) -core partitions

Huan Xiong

doi:10.1016/j.disc.2015.08.017

On the largest size of (t, t + 1, ..., t + p) -core partitions

Huan Xiong^*

^*Corresponding author for this work

University of Zurich

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

16 Scopus citations

Abstract

In this paper we prove that Amdeberhan's conjecture on the largest size of (t,t+1,t+2)-core partitions is true. We also show that the number of (t,t+1,t+2)-core partitions with the largest size is 1 or 2 based on the parity of t. More generally, the largest size of (t,t+1,...,t+p)-core partitions and the number of such partitions with the largest size are determined.

Original language	English
Pages (from-to)	308-317
Number of pages	10
Journal	Discrete Mathematics
Volume	339
Issue number	1
DOIs	https://doi.org/10.1016/j.disc.2015.08.017
State	Published - 6 Jan 2016
Externally published	Yes

Keywords

Hook length
Largest size
Partition
t-core

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Cite this

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title = "On the largest size of (t, t + 1, ..., t + p) -core partitions",

abstract = "In this paper we prove that Amdeberhan's conjecture on the largest size of (t,t+1,t+2)-core partitions is true. We also show that the number of (t,t+1,t+2)-core partitions with the largest size is 1 or 2 based on the parity of t. More generally, the largest size of (t,t+1,...,t+p)-core partitions and the number of such partitions with the largest size are determined.",

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AB - In this paper we prove that Amdeberhan's conjecture on the largest size of (t,t+1,t+2)-core partitions is true. We also show that the number of (t,t+1,t+2)-core partitions with the largest size is 1 or 2 based on the parity of t. More generally, the largest size of (t,t+1,...,t+p)-core partitions and the number of such partitions with the largest size are determined.

KW - Hook length

KW - Largest size

KW - Partition

KW - t-core

UR - https://www.scopus.com/pages/publications/84941312614

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DO - 10.1016/j.disc.2015.08.017

M3 - 文章

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VL - 339

SP - 308

EP - 317

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

ER -

On the largest size of (t, t + 1, ..., t + p) -core partitions

Abstract

Keywords

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