2019/05/27 by Sami Assaf, Assaf, Sami, Stephanie van Willigenburg +1
Mathematics · #05E05 #06A07 #14M15 #14N15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1905.11526
openalex publication_date 2019/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Young's lattice is a partial order on integer partitions whose saturated chains correspond to standard Young tableaux, one type of combinatorial object that generates the Schur basis for symmetric functions. Generalizing Young's lattice, we introduce a new partial order on weak compositions that we call the key poset. Saturated chains in this poset correspond to standard key tableaux, the combinatorial objects that generate the key polynomials, a nonsymmetric polynomial generalization of the Schur basis. Generalizing skew Schur functions, we define skew key polynomials in terms of this new poset. Using weak dual equivalence, we give a nonnegative weak composition Littlewood-Richardson rule for the key expansion of skew key polynomials, generalizing the flagged Littlewood-Richardson rule of Reiner and Shimozono.