Dual equivalence and Schur positivity
Combinatorics
2015-06-15 v3
Abstract
We define dual equivalence for any collection of combinatorial objects endowed with a descent set, and we show that giving a dual equivalence establishes the symmetry and Schur positivity of the quasi-symmetric generating function. We give an explicit formula for the Schur expansion of the generating function in terms of distinguished elements of the dual equivalence classes. These concepts and proofs simplify in the ubiquitous case when the collection of objects has a sufficiently nice reading word.
Cite
@article{arxiv.1107.0090,
title = {Dual equivalence and Schur positivity},
author = {Sami H. Assaf},
journal= {arXiv preprint arXiv:1107.0090},
year = {2015}
}
Comments
The content of this paper has been included in arXiv:1506.03798 [math.CO] (the latter to appear in Forum of Mathematics Sigma)