Sum Complexes and Uncertainty Numbers
Combinatorics
2012-12-17 v1
Abstract
Let p be a prime and let A be a subset of F_p. For k<p let X_{A,k} be the (k-1)-dimensional complex on the vertex set F_p with a full (k-2)-skeleton whose (k-1)-faces are k-subsets S of F_p such that the sum of the elements of S belongs to A. The homology groups of X_{A,k} with field coefficients are determined. In particular it is shown that if |A| \leq k then H_{k-1}(X_{A,k};F_p)=0. This implies a homological characterization of uncertainty numbers of subsets of F_p.
Cite
@article{arxiv.1212.3421,
title = {Sum Complexes and Uncertainty Numbers},
author = {Roy Meshulam},
journal= {arXiv preprint arXiv:1212.3421},
year = {2012}
}
Comments
16 pages