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A combinatorial formula for of \(\rho\)-removed uniform matroids. (English) Zbl 1450.05008
Summary: Let \(\rho\) be a non-negative integer. A \(\rho\)-removed uniform matroid is a matroid obtained from a uniform matroid by removing a collection of \(\rho\) disjoint bases. We present a combinatorial formula for Kazhdan-Lusztig polynomials of \(\rho\)-removed uniform matroids, using skew Young tableaux. Even for uniform matroids, our formula is new, gives manifestly positive integer coefficients, and is more manageable than known formulas.
05B35 Combinatorial aspects of matroids and geometric lattices
52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
05E10 Combinatorial aspects of representation theory
Full Text: DOI
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