Square integer Heffter arrays with empty cells

Archdeacon, D. S., Dinitz, J. H., Donovan, D. M. and Yazici, E. S. (2015) Square integer Heffter arrays with empty cells. Designs, Codes, and Cryptography, 77 2-3: 409-426. doi:10.1007/s10623-015-0076-4


Author Archdeacon, D. S.
Dinitz, J. H.
Donovan, D. M.
Yazici, E. S.
Title Square integer Heffter arrays with empty cells
Journal name Designs, Codes, and Cryptography   Check publisher's open access policy
ISSN 0925-1022
1573-7586
Publication date 2015
Sub-type Article (original research)
DOI 10.1007/s10623-015-0076-4
Volume 77
Issue 2-3
Start page 409
End page 426
Total pages 18
Place of publication New York, United States
Publisher Springer New York
Collection year 2016
Language eng
Formatted abstract
A Heffter array H(m,n;s,t) is an m×n matrix with nonzero entries from Z2ms+1 such that (i) each row contains s filled cells and each column contains t filled cells, (ii) every row and column sum to 0, and (iii) no element from {x,−x} appears twice. Heffter arrays are useful in embedding the complete graph K2ms+1 on an orientable surface where the embedding has the property that each edge borders exactly one s-cycle and one t-cycle. Archdeacon, Boothby and Dinitz proved that these arrays can be constructed in the case when s=m, i.e every cell is filled. In this paper we concentrate on square arrays with empty cells where every row sum and every column sum is 0 in Z. We solve most of the instances of this case.
Keyword Biembedding
Heffter array
Cycle system
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
 
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