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Twisted Incidence Algebras and Kazhdan–Lusztig–Stanley Functions

✍ Scribed by Francesco Brenti

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 284 KB
Volume: 148
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1999.1839

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✦ Synopsis

We introduce a new multiplication in the incidence algebra of a partially ordered set and study the resulting algebra. As an application of the properties of this algebra we obtain a combinatorial formula for the Kazhdan Lusztig Stanley functions of a poset. As special cases this yields new combinatorial formulas for the parabolic and inverse parabolic Kazhdan Lusztig polynomials, for the generalized (toric) h-vector of an Eulerian poset and for the Lusztig Vogan polynomials.

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