Geodesic
Intersection cohomology of the symmetric reciprocal plane
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 129-138.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 $[n-2i,2,\dots,2]$.
Classification : 05E15, 05E10, 05B35
Keywords: intersection cohomology, reciprocal plane, Kazhdan-Lusztig polynomial, matroid 
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Proudfoot, Nicholas; Wakefield, Max; Young, Ben. Intersection cohomology of the symmetric reciprocal plane. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 129-138. http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a5/