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Some Schubert shenanigans

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arxiv 1704.00851 v2 pith:DDY5VROO submitted 2017-04-04 math.CO

Richard P. Stanley This is my paper · ORCID
classification math.CO
keywords schuberttildecertainconjectureconjectureddeterminantdiscusseddots
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abstract

We give a conjectured evaluation of the determinant of a certain matrix $\tilde{D}(n,k)$. The entries of $\tilde{D}(n,k)$ are either 0 or specializations $\mathfrak{S}_w(1,\dots,1)$ of Schubert polynomials. The conjecture implies that the weak order of the symmetric group $S_n$ has the strong Sperner property. A number of peripheral results and problems are also discussed.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Signed puzzles for Schubert coefficients

    math.CO 2025-04 conditional novelty 7.0 of 10

    A signed tiling rule computes every Schubert coefficient, and the rule implies a new polynomiality result for coefficient sums with bounded inversions.

  2. Schubert polynomials and patterns in permutations

    math.CO 2024-12 conditional novelty 6.0 of 10

    A new lower bound relates the number of supports of Schubert polynomials to weighted counts of twelve permutation patterns, strengthening previous 132 and 1432 bounds.

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