The Gaussian coefficient revisited

Richard Ehrenborg; Margaret A. Readdy

The Gaussian coefficient revisited

Mathematics

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

2 Scopus citations

Abstract

We give a new q-(1 + q)-analogue of the Gaussian coefficient, also known as the q- binomial which, like the original q-binomial [n/k]_q, is symmetric in k and n-k. We show this q-(1+q)-binomial is more compact than the one discovered by Fu, Reiner, Stanton, and Thiem. Underlying our q-(1 + q)-analogue is a Boolean algebra decomposition of an associated poset. These ideas are extended to the Birkhoff transform of any finite poset. We end with a discussion of higher analogues of the q-binomial.

Original language	English
Article number	16.7.8
Journal	Journal of Integer Sequences
Volume	19
Issue number	7
State	Published - Jan 1 2016

Bibliographical note

Publisher Copyright:
© 2016, University of Waterloo. All rights reserved.

Funding

The authors thank the referee for helpful comments. This work was partially supported by a grant from the Simons Foundation (#206001 to Margaret Readdy).

Funders	Funder number
Simons Foundation	206001

Keywords

Birkhoff transform
Distributive lattice
Poset decomposition
Q-analogue

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

Cite this

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title = "The Gaussian coefficient revisited",

abstract = "We give a new q-(1 + q)-analogue of the Gaussian coefficient, also known as the q- binomial which, like the original q-binomial [n/k]q, is symmetric in k and n-k. We show this q-(1+q)-binomial is more compact than the one discovered by Fu, Reiner, Stanton, and Thiem. Underlying our q-(1 + q)-analogue is a Boolean algebra decomposition of an associated poset. These ideas are extended to the Birkhoff transform of any finite poset. We end with a discussion of higher analogues of the q-binomial.",

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N2 - We give a new q-(1 + q)-analogue of the Gaussian coefficient, also known as the q- binomial which, like the original q-binomial [n/k]q, is symmetric in k and n-k. We show this q-(1+q)-binomial is more compact than the one discovered by Fu, Reiner, Stanton, and Thiem. Underlying our q-(1 + q)-analogue is a Boolean algebra decomposition of an associated poset. These ideas are extended to the Birkhoff transform of any finite poset. We end with a discussion of higher analogues of the q-binomial.

AB - We give a new q-(1 + q)-analogue of the Gaussian coefficient, also known as the q- binomial which, like the original q-binomial [n/k]q, is symmetric in k and n-k. We show this q-(1+q)-binomial is more compact than the one discovered by Fu, Reiner, Stanton, and Thiem. Underlying our q-(1 + q)-analogue is a Boolean algebra decomposition of an associated poset. These ideas are extended to the Birkhoff transform of any finite poset. We end with a discussion of higher analogues of the q-binomial.

KW - Birkhoff transform

KW - Distributive lattice

KW - Poset decomposition

KW - Q-analogue

UR - https://www.scopus.com/pages/publications/84995624318

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M3 - Article

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JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

IS - 7

M1 - 16.7.8

ER -

The Gaussian coefficient revisited

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

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Cite this