The existence of square non-integer Heffter arrays

2018/08/08 by Nicholas J. Cavenagh, Jeff Dinitz, Cavenagh, Nicholas J. +5 · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1808.02588

openalex publication_date 2018/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Heffter array H(n;k) is an n× n matrix such that each row and column contains k filled cells, each row and column sum is divisible by 2nk+1 and either x or -x appears in the array for each integer 1≤ x≤ nk. Heffter arrays are useful for embedding the graph K_2nk+1 on an orientable surface. An integer Heffter array is one in which each row and column sum is 0. Necessary and sufficient conditions (on n and k) for the existence of an integer Heffter array H(n;k) were verified by Archdeacon, Dinitz, Donovan and Yazıcı (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 3≤ k

Citations

• On Partial Sums in Cyclic Groups

Cited by

• Globally Simple Heffter Arrays H(n;k) with k ≡ 1 \pmod4

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