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Ehrenborg, Richard; Goresky, Mark; Readdy, Margaret
Discrete mathematics and theoretical computer science, 01/2013, Volume: DMTCS Proceedings vol. AS,..., Issue: ProceedingsJournal Article
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. Nous montrons le $\mathrm{cd}$-index existe pour les manifolds de Whitney stratifiées en élargissant la notion d’un poset gradué à celle qu'un poset quasi-gradué. C’est un poset doté d'une fonction de rang que préservant l’ordre du poset et une fonction de zêta pondérée. Ceci nous permet de généraliser la notion classique de “Eulerianness”, et obtenir un $\mathrm{cd}$-index dans l’arène des posets quasi-gradués. Nous tenons également à l’opération de semi-suspension pour que d’intégrer une complexe dans la frontière d’une balle de dimension supérieur et étudions les composants shelling d’un simplex.
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