The Gaussian coefficient revisited

Richard Ehrenborg; Margaret A. Readdy

The Gaussian coefficient revisited

Mathematics

Producción científica: Article › revisión exhaustiva

2 Citas (Scopus)

Resumen

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.

Idioma original	English
Número de artículo	16.7.8
Publicación	Journal of Integer Sequences
Volumen	19
N.º	7
Estado	Published - ene 1 2016

Nota bibliográfica

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

Financiación

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

Financiadores	Número del financiador
Simons Foundation	206001

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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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.

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KW - Distributive lattice

KW - Poset decomposition

KW - Q-analogue

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ER -

The Gaussian coefficient revisited

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

Otros archivos y enlaces

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