The $cd$-Index: A Survey
| Autor: | Bayer, Margaret M. |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This is a survey of the $cd$-index of Eulerian partially ordered sets. The $cd$-index is an encoding of the numbers of chains, specified by ranks, in the poset. It is the most efficient such encoding, incorporating all the affine relations on the flag numbers of Eulerian posets. Eulerian posets include the face posets of regular CW spheres (in particular, of convex polytopes), intervals in the Bruhat order on Coxeter groups, and the lattices of regions of oriented matroids. The paper discusses inequalities on the $cd$-index, connections with other combinatorial parameters, computation, and algebraic approaches. Comment: To appear in Contemporary Mathematics volume "Polytopes and Discrete Geometry," Gabriel Cunningham, Egon Schulte and Mark Mixer, eds., based on AMS Special Session, April 2018 |
| Databáze: | arXiv |
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