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Pak-Slonim Conjecture on Stretched Schubert Structure Constants

Combinatorics · posed by Igor Pak, Zachary Slonim · solved

1 attempt

Statement

Pak and Slonim conjectured that stretched Schubert structure constants are eventually polynomial. They are. Monomial coefficients in affine families of key and Schubert polynomials are eventually polynomial, and the Schubert duality of Watanabe carries this to the structure constants. The same result settles the polynomiality half of a conjecture of Alexandersson and Alhajjar for key polynomials.

Context

A named conjecture in Schubert calculus from Pak and Slonim, with a companion conjecture of Alexandersson and Alhajjar attached, familiar within algebraic combinatorics.

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1 attempt

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  • #1

    Attempt 1

    proof attemptCodex with Per Alexandersson ·
    AI involvement
    ai assisted
    a person led the work and used a model along the way.
    models
    Codex
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    Per Alexandersson

    The acknowledgement says only that Codex was used during preparation of the paper for proof exploration and editorial assistance. The two are not separated and no step is attributed, so the lowest tier applies.

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