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Mathematics > Combinatorics

arXiv:1801.00399 (math)
[Submitted on 1 Jan 2018 (v1), last revised 20 Feb 2021 (this version, v6)]

Title:Computation of Maximal Determinants of Binary Circulant Matrices

Authors:Richard P. Brent, Adam B. Yedidia
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Abstract:We describe algorithms for computing maximal determinants of binary circulant matrices of small orders. Here "binary matrix" means a matrix whose elements are drawn from $\{0,1\}$ or $\{-1,1\}$. We describe efficient parallel algorithms for the search, using Duval's algorithm for generation of necklaces and the well-known representation of the determinant of a circulant in terms of roots of unity. Tables of maximal determinants are given for orders $\le 53$. Our computations extend earlier results and disprove two plausible conjectures.
Comments: 22 pages, 4 tables. Improved analysis of quantile estimation in v4, Table 2 updated in v5, Table 4 updated in v6
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
MSC classes: 05A15 (Primary) 05A19, 65T50 (Secondary)
Cite as: arXiv:1801.00399 [math.CO]
  (or arXiv:1801.00399v6 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1801.00399
Journal reference: Journal of Integer Sequences 21 (2018), article 18.5.6, 19 pp

Submission history

From: Richard Brent [view email]
[v1] Mon, 1 Jan 2018 06:32:50 UTC (15 KB)
[v2] Wed, 10 Jan 2018 00:42:30 UTC (15 KB)
[v3] Thu, 19 Apr 2018 05:39:17 UTC (19 KB)
[v4] Wed, 6 Jun 2018 13:57:13 UTC (20 KB)
[v5] Tue, 11 Jun 2019 06:26:13 UTC (20 KB)
[v6] Sat, 20 Feb 2021 02:05:05 UTC (19 KB)
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