The $Z$-Polynomial of a Matroid
Keyword(s):
We introduce the $Z$-polynomial of a matroid, which we define in terms of the Kazhdan-Lusztig polynomial. We then exploit a symmetry of the $Z$-polynomial to derive a new recursion for Kazhdan-Lusztig coefficients. We solve this recursion, obtaining a closed formula for Kazhdan-Lusztig coefficients as alternating sums of multi-indexed Whitney numbers. For realizable matroids, we give a cohomological interpretation of the $Z$-polynomial in which the symmetry is a manifestation of Poincaré duality.
2006 ◽
Vol 116
(3)
◽
pp. 293-298
2016 ◽
Vol 152
(7)
◽
pp. 1398-1420
◽
1989 ◽
Vol s2-39
(2)
◽
pp. 271-284
◽
2003 ◽
Vol 2003
(38)
◽
pp. 2425-2445
◽
Keyword(s):
1981 ◽
Vol 81
(3)
◽
pp. 353-353