The existence of square non-integer Heffter arrays
Combinatorics
2018-08-09 v1
Abstract
A Heffter array is an matrix such that each row and column contains filled cells, each row and column sum is divisible by and either or appears in the array for each integer . Heffter arrays are useful for embedding the graph on an orientable surface. An integer Heffter array is one in which each row and column sum is . Necessary and sufficient conditions (on and ) for the existence of an integer Heffter array were verified by Archdeacon, Dinitz, Donovan and Yaz\i c\i \ (2015) and Dinitz and Wanless (2017). In this paper we consider square Heffter arrays that are not necessarily integer. We show that such Heffter arrays exist whenever .
Cite
@article{arxiv.1808.02588,
title = {The existence of square non-integer Heffter arrays},
author = {Nicholas J. Cavenagh and Jeff Dinitz and Diane Donovan and Sule Yazıcı},
journal= {arXiv preprint arXiv:1808.02588},
year = {2018}
}