Further constructions of square integer relative Heffter arrays

2025/09/12 by Diane Donovan, Donovan, Diane, S.S. Lawson +3
Computer Science · Engineering · #05B20 #Antenna Design and Optimization #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2509.09907

openalex publication_date 2025/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A square integer relative Heffter array is an n × n array whose rows and columns sum to zero, each row and each column has exactly k entries and either x or -x appears in the array for every x ∈ ℤ_2nk+t∖ J, where J is a subgroup of size t. There are many open problems regarding the existence of these arrays. In this paper we construct two new infinite families of these arrays with the additional property that they are strippable. These constructions complete the existence theory for square integer relative Heffter arrays in the case where k=3 and n is prime.

Citations

• On relative simple Heffter spaces
• Heffter Spaces
• A survey of Heffter arrays
• On the existence of integer relative Heffter arrays
• Relative Heffter arrays and biembeddings
• A generalization of Heffter arrays
• Square Integer Heffter Arrays with Empty Cells
• Heffter Arrays and Biembedding Graphs on Surfaces

Related

• A generalization of Heffter arrays
• The existence of square non-integer Heffter arrays
• On the existence of integer relative Heffter arrays
• Towards a solution of Archdeacon's conjecture on integer Heffter arrays
• Tight Heffter Arrays Exist for all Possible Values: The Research Report