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GENUS 0 AND 1 HURWITZ NUMBERS: RECURSIONS, FORMULAS, AND GRAPH-THEORETIC INTERPRETATIONS
RECURSIONS FORMULAS GRAPH-THEORETIC
2015/7/14
We derive a closed-form expression for all genus 1 Hurwitz numbers, and give a
simple new graph-theoretic interpretation of Hurwitz numbers in genus 0 and 1. (Hurwitz
numbers essentially count irred...
Supercharacter formulas for pattern groups。
Factorization formulas for higher depth determinants of the Laplacian on the n-sphere
depth determinants the Laplacian on the n-sphere
2010/11/19
We explicitly give factorization formulas for higher depth determinants, which are defined via derivatives of the spectral zeta function at non-positive integer points, of Laplacians on the n-sphere i...
Mask formulas for cograssmannian Kazhdan-Lusztig polynomials
Mask formulas cograssmannian Kazhdan-Lusztig polynomials
2010/11/11
We give two contructions of sets of masks on cograssmannian permutations that can be used in Deodhar's formula for Kazhdan-Lusztig basis elements of the Iwahori-Hecke algebra. The constructions are re...