The Gaussian coefficient revisited

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2 Scopus citations


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 languageEnglish
Article number16.7.8
JournalJournal of Integer Sequences
Issue number7
StatePublished - Jan 1 2016

Bibliographical note

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


  • Birkhoff transform
  • Distributive lattice
  • Poset decomposition
  • Q-analogue

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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