Geodesic
A combinatorial formula for Kazhdan-Lusztig polynomials of sparse paving matroids
Kyungyong Lee1 ; George D. Nasr2 ; Jamie Radcliffe3
1University of Alabama
2Universty of Nebraksa--Lincoln
3University of Nebraska-Lincoln
The electronic journal of combinatorics, Tome 28 (2021) no. 4
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We present a combinatorial formula using skew Young tableaux for the coefficients of Kazhdan-Lusztig polynomials for sparse paving matroids. These matroids are known to be logarithmically almost all matroids, but are conjectured to be almost all matroids. We also show the positivity of these coefficients using our formula. In special cases, such as uniform matroids, our formula has a nice combinatorial interpretation.
DOI : 10.37236/10602
Classification : 05B35, 05E10
Mots-clés : skew Young tableaux, algebro-geometric method

Kyungyong Lee  1   ; George D. Nasr  2   ; Jamie Radcliffe  3

1 University of Alabama
2 Universty of Nebraksa--Lincoln
3 University of Nebraska-Lincoln 
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     author = {Kyungyong Lee and George D. Nasr and Jamie Radcliffe},
     title = {A combinatorial formula for {Kazhdan-Lusztig} polynomials of sparse paving matroids},
     journal = {The electronic journal of combinatorics},
     year = {2021},
     volume = {28},
     number = {4},
     doi = {10.37236/10602},
     zbl = {1486.05037},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/10602/}
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Kyungyong Lee; George D. Nasr; Jamie Radcliffe. A combinatorial formula for Kazhdan-Lusztig polynomials of sparse paving matroids. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/10602

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