On the Support of Grothendieck Polynomials

Mészáros, Karola; Setiabrata, Linus; Dizier, Avery St.

doi:10.1007/s00026-024-00712-3

Ann. Comb.

2024

DOI: 10.1007/s00026-024-00712-3

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On the Support of Grothendieck Polynomials

Karola Mészáros,

Linus Setiabrata,

Avery St. Dizier

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2024

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An inverse Grassmannian Littlewood–Richardson rule and extensions

Pechenik,

Weigandt

2024

Forum of Mathematics, Sigma

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Chow rings of flag varieties have bases of Schubert cycles $\sigma _u $ , indexed by permutations. A major problem of algebraic combinatorics is to give a positive combinatorial formula for the structure constants of this basis. The celebrated Littlewood–Richardson rules solve this problem for special products $\sigma _u \cdot \sigma _v$ , where u and v are p-Grassmannian permutations. Building on work of Wyser, we introduce backstable clans to prove such a rule for the problem of computing the product $\sigma _u \cdot \sigma _v$ when u is p-inverse Grassmannian and v is q-inverse Grassmannian. By establishing several new families of linear relations among structure constants, we further extend this result to obtain a positive combinatorial rule for $\sigma _u \cdot \sigma _v$ in the case that u is covered in weak Bruhat order by a p-inverse Grassmannian permutation and v is a q-inverse Grassmannian permutation.

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An inverse Grassmannian Littlewood–Richardson rule and extensions

Pechenik,

Weigandt

2024

Forum of Mathematics, Sigma

View full text Add to dashboard Cite

show abstract

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On the Support of Grothendieck Polynomials

Cited by 1 publication

References 26 publications

An inverse Grassmannian Littlewood–Richardson rule and extensions

An inverse Grassmannian Littlewood–Richardson rule and extensions

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