×

zbMATH — the first resource for mathematics

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.
MSC:
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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] T. Braden, A. Vysogorets,Kazhdan-Lusztig oolynomials of matroids under deletion. Electron. J. Combin. 27 (2020), no. 1, #P1.17,arXiv:1909.09888. · Zbl 1431.05150
[2] B. Elias, N. Proudfoot, M. Wakefield,The Kazhdan-Lusztig polynomial of a matroid. Adv. Math. 299 (2016), 36-70. · Zbl 1341.05250
[3] K. Gedeon,Kazhdan-Lusztig polynomials of thagomizer matroids. Electron. J. Combin. 24 (2017), no. 3, #P3.12. · Zbl 1369.05029
[4] A. Gao, L. Lu, M. Xie, A. Yang, P. Zhang,The Kazhdan-Lusztig polynomials of uniform matroids.arXiv:1806.10852.
[5] K. Gedeon, N. Proudfoot, B. Young,The equivariant Kazhdan-Lusztig polynomial of a matroid.J. Combin. Theory Ser. A 150 (2017), 267-294. · Zbl 1362.05131
[6] K. Gedeon, N. Proudfoot, B. Young,Kazhdan-Lusztig polynomials of matroids: a survey of results and conjectures.S´em. Lothar. Combin. 78B (2017), Art. 80, 12 pp. arXiv:1806.10852. · Zbl 1384.05172
[7] T. Karn, M. Wakefield,Stirling numbers in braid matroid Kazhdan-Lusztig polynomials. Adv. in Appl. Math. 103 (2019), 1-12. · Zbl 1402.05031
[8] L. Lu, M. Xie, A. Yang,Kazhdan-Lusztig polynomials of fan matroids, wheel matroids and whirl matroids.arXiv:1802.03711.
[9] N. Proudfoot,The algebraic geometry of Kazhdan-Lusztig-Stanley polynomials. EMS Surv. Math. Sci. 5 (2018), no. 1, 99-127. · Zbl 1445.14038
[10] N. Proudfoot,Equivariant Kazhdan-Lusztig polynomials ofq-niform matroids.Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 613-619.arXiv:1808.07855. · Zbl 1417.05024
[11] R. Stanley,Polygon dissections and standard Young tableaux. Journal of Combinatorial Theory, series A76(1996), 175-177. · Zbl 0859.05075
[12] M. Wakefield,Partial flag incidence algebras.arXiv:1605.01685.
[13] M.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.