2017/02/14 by Sami Assaf, Assaf, Sami · 1 citation
Agricultural and Biological Sciences · Mathematics · #05A19 #05E10 #05E18 #14N15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Botanical Research and Chemistry #Combinatorics (math.CO) #FOS: Mathematics #Primary 05E05 #Secondary 05A15
paper · pdf · doi:10.48550/arxiv.1702.04051
openalex publication_date 2017/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use dual equivalence to give a short, combinatorial proof that Stanley symmetric functions are Schur positive. We introduce weak dual equivalence, and use it to give a short, combinatorial proof that Schubert polynomials are key positive. To demonstrate further the utility of this new tool, we use weak dual equivalence to prove a nonnegative Littlewood--Richardson rule for the key expansion of the product of a key polynomial and a Schur polynomial, and to introduce skew key polynomials that, when skewed by a partition, expand nonnegatively in the key basis.