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Intersection cohomology of the symmetric reciprocal plane. (English) Zbl 1331.05233

Summary: We compute the Kazhdan-Lusztig polynomial of the uniform matroid of rank \(n-1\) on \(n\) elements by proving that the coefficient of \(t^i\) is equal to the number of ways to choose \(i\) non-intersecting chords in an \((n-i+1)\)-gon. We also show that the corresponding intersection cohomology group is isomorphic to the irreducible representation of \(S_n\) associated with the partition \([n-2i,2,\dots,2]\).

MSC:

05E15 Combinatorial aspects of groups and algebras (MSC2010)
05E10 Combinatorial aspects of representation theory
05B35 Combinatorial aspects of matroids and geometric lattices

Software:

OEIS; SageMath
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References:

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