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Euler flag enumeration of Whitney stratified spaces

Abstract : We show the $\mathrm{cd}$-index exists for Whitney stratified manifolds by extending the notion of a graded poset to that of a quasi-graded poset. This is a poset endowed with an order-preserving rank function and a weighted zeta function. This allows us to generalize the classical notion of Eulerianness, and obtain a $\mathrm{cd}$-index in the quasi-graded poset arena. We also extend the semi-suspension operation to that of embedding a complex in the boundary of a higher dimensional ball and study the shelling components of the simplex.
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https://hal.inria.fr/hal-01229715
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:20:28 AM
Last modification on : Friday, August 9, 2019 - 4:26:05 PM
Long-term archiving on: : Thursday, February 18, 2016 - 11:43:12 AM

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Richard Ehrenborg, Mark Goresky, Margaret Readdy. Euler flag enumeration of Whitney stratified spaces. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.133-144. ⟨hal-01229715⟩

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