Richard Ehrenborg ; Mark Goresky ; Margaret Readdy - Euler flag enumeration of Whitney stratified spaces

dmtcs:12799 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.12799
Euler flag enumeration of Whitney stratified spacesArticle

Authors: Richard Ehrenborg ORCID1; Mark Goresky 2; Margaret Readdy ORCID1

  • 1 Department of Mathematics
  • 2 School of Mathematics [Princeton]

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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Eulerian condition,quasi-graded poset,semisuspension,weighted zeta function,Whitney's conditions A and B.,[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • CDI Type II: Pseudorandomness; Funder: National Science Foundation; Code: 0835373
  • Bruhat and balanced graphs, manifolds, partitions and affine permutations; Funder: National Science Foundation; Code: 0902063
  • Collaborative Research: Understanding, Coping with, and Benefiting from Intractibility.; Funder: National Science Foundation; Code: 0832797

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