On powers of 2 dividing the values of certain plane partition functions

Darrin D. Frey; James A. Sellers

On powers of 2 dividing the values of certain plane partition functions

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

Abstract

We consider two families of plane partitions: totally symmetric self-complementary plane partitions (TSSCPPs) and cyclically symmetric transpose complement plane partitions (CSTCPPs). If T(n) and C(n) are the numbers of such plane partitions in a 2n × 2n × 2n box, then ord ₂(T(n)) = ord ₂(C(n)) for all n ≥ 1. We also discuss various consequences, along with other results on ord ₂(T(n)).

Original language	English (US)
Journal	Journal of Integer Sequences
Volume	4
Issue number	1
State	Published - Dec 1 2001
Externally published	Yes

Keywords

Alternating sign matrices
CSTCPP
Cyclically symmetric transpose complement plane partitions
Jacobsthal numbers
TSSCPP
Totally symmetric self-complementary plane partitions

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AB - We consider two families of plane partitions: totally symmetric self-complementary plane partitions (TSSCPPs) and cyclically symmetric transpose complement plane partitions (CSTCPPs). If T(n) and C(n) are the numbers of such plane partitions in a 2n × 2n × 2n box, then ord 2(T(n)) = ord 2(C(n)) for all n ≥ 1. We also discuss various consequences, along with other results on ord 2(T(n)).

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KW - Cyclically symmetric transpose complement plane partitions

KW - Jacobsthal numbers

KW - TSSCPP

KW - Totally symmetric self-complementary plane partitions

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On powers of 2 dividing the values of certain plane partition functions

Abstract

Keywords

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