Combinatorics of `unavoidable complexes'

2016/12/30 by Milutinović, Marija Jelić, Jojić, Duško, Timotijević, Marinko +2
#05E45 #52A35 #55U10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.09487

Abstract

The partition number π(K) of a simplicial complex K⊂ 2^[n] is the minimum integer ν such that for each partition A₁\uplus…\uplus A_ν= [n] of [n] at least one of the sets A_i is in K. A complex K is r-unavoidable if π(K)≤ r. Motivated by the problems of Tverberg-Van Kampen-Flores type, and inspired by the `constraint method' of Blagojević, Frick, and Ziegler, arXiv:1401.0690 [math.CO], we study the combinatorics of r-unavoidable complexes.

Related

• Topology of unavoidable complexes
• Partition and Cohen-Macaulay Extenders
• Classifications of ℓ-Zero-Sumfree Sets
• The Partition Complex: an invitation to combinatorial commutative algebra
• A balanced non-partitionable Cohen-Macaulay complex