Christopher Severs ; Jacob A. White - The Homology of the Real Complement of a $k$-parabolic Subspace Arrangement

dmtcs:2882 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2882
The Homology of the Real Complement of a $k$-parabolic Subspace ArrangementArticle

Authors: Christopher Severs 1; Jacob A. White 2

The $k$-parabolic subspace arrangement, introduced by Barcelo, Severs and White, is a generalization of the well known $k$-equal arrangements of type-$A$ and type-$B$. In this paper we use the discrete Morse theory of Forman to study the homology of the complements of $k$-parabolic subspace arrangements. In doing so, we recover some known results of Björner et al. and provide a combinatorial interpretation of the Betti numbers for any $k$-parabolic subspace arrangement. The paper provides results for any $k$-parabolic subspace arrangement, however we also include an extended example of our methods applied to the $k$-equal arrangements of type-$A$ and type-$B$. In these cases, we obtain new formulas for the Betti numbers.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Subspace Arrangements,Discrete Morse Theory,Coxeter Groups,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Consultation statistics

This page has been seen 164 times.
This article's PDF has been downloaded 180 times.