• Publications
  • Influence
On Embedding Incomplete Symmetric Latin Squares
  • A. B. Cruse
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1974
TLDR
We show that any incomplete n × n symmetric Latin square can be embedded in a complete symmetric diagonal Latin square of order 2 n + 1. Expand
  • 72
  • 2
On linear programming duality and Landau’s characterization of tournament
Abstract H. G. Landau has characterized those integer-sequences S = (s1, s2, . . . , sn) which can arise as score-vectors in an ordinary round-robin tournament among n contestants [17]. If s1 ≤ s2 ≤Expand
  • 3
  • 2
  • PDF
On removing a vertex from the assignment polytope
Abstract Necessary and sufficient conditions are given for a doubly stochastic matrix D to be expressible as a convex combination of permutation matrices distinct from the identity, thus solving aExpand
  • 10
  • 1
Some combinatorial properties of centrosymmetric matrices
Abstract The elements in the group of centrosymmetric n × n permutation matrices are the extreme points of a convex subset of n 2 -dimensional Euclidean space, which we characterize by a very simpleExpand
  • 17
  • 1
A note on symmetric doubly-stochastic matrices
  • A. B. Cruse
  • Computer Science, Mathematics
  • Discret. Math.
  • 1975
TLDR
Each extreme point in the convex set @D^*"n of all nxn symmetric doubly-stochastic matrices is shown to have the form 12(P + P^t), for some nx n permutation matrix P. Expand
  • 19
  • 1
A Number-Theoretic Function Related to Latin Squares
  • A. B. Cruse
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1 November 1975
  • 4
  • 1
On the Finite Completion of Partial Latin Cubes
  • A. B. Cruse
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1 July 1974
TLDR
We prove that any finite partial latin square (or hyper-cube) can be embedded in a finite latin cube (hyper-cube). Expand
  • 21
Small Embeddings for Partial Semisymmetric and Totally Symmetric Quasigroups
In 1960 Trevor Evans proved that a finite partial quasigroup of order n could be embedded in a finite quasigroup of order In [4]. Evans' Theorem on the finite embeddability of partial quasigroups wasExpand
  • 13
A note on 1-factors in certain regular multigraphs
  • A. B. Cruse
  • Computer Science, Mathematics
  • Discret. Math.
  • 1977
TLDR
This stronger version of Berge's theorem follows easily from a theorem on doubly-stochastic matrices proved previously. Expand
  • 4
A proof of Fulkerson's characterization of permutation matrices
Abstract A method is described for obtaining the facets of certain convex polyhedra from the optimal solutions to a related linear programming problem. This approach provides a direct proof, via theExpand
  • 9
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