Geodesic
Polynomials defined by tableaux and linear recurrences
Per Alexandersson1
1Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, U.S.A.
The electronic journal of combinatorics, Tome 23 (2016) no. 1
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We show that several families of polynomials defined via fillings of diagrams satisfy linear recurrences under a natural operation on the shape of the diagram. We focus on key polynomials, (also known as Demazure characters), and Demazure atoms. The same technique can be applied to Hall-Littlewood polynomials and dual Grothendieck polynomials.The motivation behind this is that such recurrences are strongly connected with other nice properties, such as interpretations in terms of lattice points in polytopes and divided difference operators.
DOI : 10.37236/5284
Classification : 05E10, 05E05
Mots-clés : linear recurrences, Schur polynomials, key polynomials, Demazure characters, Demazure atoms, Schubert polynomials, Grothendieck polynomials, Hall-Littlewood polynomials, Young tableaux

Per Alexandersson  1

1 Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, U.S.A. 
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     title = {Polynomials defined by tableaux and linear recurrences},
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     doi = {10.37236/5284},
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Per Alexandersson. Polynomials defined by tableaux and linear recurrences. The electronic journal of combinatorics, Tome 23 (2016) no. 1. doi: 10.37236/5284

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