Combinatorics of `unavoidable complexes'

Marija Jelić Milutinović; Duško Jojić; Marinko Timotijević; Siniša T. Vrećica; Rade T. Živaljević

Combinatorics of `unavoidable complexes'

Combinatorics 2019-05-14 v2

Authors: Marija Jelić Milutinović , Duško Jojić , Marinko Timotijević , Siniša T. Vrećica , Rade T. Živaljević

Abstract

The partition number $\pi(K)$ of a simplicial complex $K\subset 2^{[n]}$ is the minimum integer $\nu$ such that for each partition $A_1\uplus\ldots\uplus A_\nu = [n]$ of $[n]$ at least one of the sets $A_i$ is in $K$ . A complex $K$ is $r$ -unavoidable if $\pi(K)\leq r$ . Motivated by the problems of Tverberg-Van Kampen-Flores type, and inspired by the `constraint method' of Blagojevi\'{c}, Frick, and Ziegler, arXiv:1401.0690 [math.CO], we study the combinatorics of $r$ -unavoidable complexes.

Keywords

combinatorial bounds and extremal problems partition theory computational complexity

Cite

@article{arxiv.1612.09487,
  title  = {Combinatorics of `unavoidable complexes'},
  author = {Marija Jelić Milutinović and Duško Jojić and Marinko Timotijević and Siniša T. Vrećica and Rade T. Živaljević},
  journal= {arXiv preprint arXiv:1612.09487},
  year   = {2019}
}

Comments

This paper is an offspring of the unpublished preprint arXiv:1603.08472 [math.AT]

Combinatorics of `unavoidable complexes'

Abstract

Keywords

Cite

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