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Prism tableaux for alternating sign matrix varieties

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arxiv 1708.07236 v1 pith:VFL4W567 submitted 2017-08-24 math.CO math.AG

Anna Weigandt This is my paper · ORCID
classification math.COmath.AG
keywords tableauxmatrixprismalternatingformulasignvarietiespolynomials
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A prism tableau is a set of reverse semistandard tableaux, each positioned within an ambient grid. Prism tableaux were introduced to provide a formula for the Schubert polynomials of A. Lascoux and M.P. Sch\"utzenberger. This formula directly generalizes the well known expression for Schur polynomials as a sum over semistandard tableaux. Alternating sign matrix varieties generalize the matrix Schubert varieties of W. Fulton. We use prism tableaux to give a formula for the multidegree of an alternating sign matrix variety.

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  1. Weak order: Alternating sign matrices, monotone triangles, and bumpless pipe dreams

    math.CO 2026-06 unverdicted novelty 6.0 of 10

    The paper establishes equivalence between two prior definitions of weak order on ASM(n) and gives three explicit combinatorial descriptions of its covering relations plus a fiber characterization via bumpless pipe dreams.

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