On Elser's conjecture and the topology of $U$-nucleus complex

Abstract

Dorpalen-Barry et al. proved Elser's conjecture about sign of Elser's number by interpreting them as certain sums of reduced Euler characteristics of an abstract simplicial complex known as $U$-nucleus complex. We prove a conjecture posed by them regarding the homology of $U$-nucleus complex.

8 pages, 8 figures

References in corpus (1)

• A positivity phenomenon in Elser's Gaussian-cluster percolation model

Cited by in corpus (1)

• A note on an application of discrete Morse theoretic techniques on the complex of disconnected graphs