Dual equivalence graphs I: A new paradigm for Schur positivity
Combinatorics
2020-03-05 v1
Abstract
We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. This provides a universal method for establishing the symmetry and Schur positivity of quasisymmetric functions.
Keywords
Cite
@article{arxiv.1506.03798,
title = {Dual equivalence graphs I: A new paradigm for Schur positivity},
author = {Sami H. Assaf},
journal= {arXiv preprint arXiv:1506.03798},
year = {2020}
}
Comments
24 pages, 27 figures, to appear in Forum of Mathematics, Sigma. arXiv admin note: substantial text overlap with arXiv:1005.3759