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arxiv: 1708.07236 · v1 · submitted 2017-08-24 · 🧮 math.CO · math.AG

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Prism tableaux for alternating sign matrix varieties

Anna Weigandt

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classification 🧮 math.CO math.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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