The theory and application of Latin bitrades: a survey
NJ Cavenagh - Mathematica Slovaca, 2008 - Springer
A latin bitrade is a pair of partial latin squares which are disjoint, occupy the same set of non-
empty cells, and whose corresponding rows and columns contain the same sets of symbols …
empty cells, and whose corresponding rows and columns contain the same sets of symbols …
[HTML][HTML] The set of autotopisms of partial Latin squares
RM Falcón - Discrete Mathematics, 2013 - Elsevier
Symmetries of a partial Latin square are primarily determined by its autotopism group.
Analogously to the case of Latin squares, given an isotopism Θ, the cardinality of the set …
Analogously to the case of Latin squares, given an isotopism Θ, the cardinality of the set …
[HTML][HTML] Critical sets for Sudoku and general graph colorings
J Cooper, A Kirkpatrick - Discrete Mathematics, 2014 - Elsevier
We discuss the problem of finding critical sets in graphs, a concept which has appeared in a
number of guises in the combinatorics and graph theory literature. The case of the Sudoku …
number of guises in the combinatorics and graph theory literature. The case of the Sudoku …
Teaching dimension, VC dimension, and critical sets in Latin squares
A critical set in an $ n\times n $ Latin square is a minimal set of entries that uniquely
identifies it among all Latin squares of the same size. It is conjectured by Nelder in 1979 …
identifies it among all Latin squares of the same size. It is conjectured by Nelder in 1979 …
Completing latin squares: critical sets II
Completing Latin squares: Critical sets II Page 1 Completing Latin Squares: Critical Sets II Peter
Horak,1 Italo J. Dejter2 1University of Washington, Tacoma, Tacoma, WA 98402-3100, E-mail …
Horak,1 Italo J. Dejter2 1University of Washington, Tacoma, Tacoma, WA 98402-3100, E-mail …
On the spectrum of critical sets in latin squares of order 2n
D Donovan, J LeFevre… - Journal of Combinatorial …, 2008 - Wiley Online Library
Suppose that L is a latin square of order m and P⊑ L is a partial latin square. If L is the only
latin square of order m which contains P, and no proper subset of P has this property, then P …
latin square of order m which contains P, and no proper subset of P has this property, then P …
The maximum, supremum, and spectrum for critical set sizes in (0, 1)‐matrices
NJ Cavenagh, LK Wright - Journal of Combinatorial Designs, 2019 - Wiley Online Library
If is a partially filled‐in (0, 1)‐matrix with a unique completion to a (0, 1)‐matrix (with
prescribed row and column sums), then we say that is a defining set for. A critical set is a …
prescribed row and column sums), then we say that is a defining set for. A critical set is a …
[HTML][HTML] Latin trades on three or four rows
R Bean - Discrete mathematics, 2006 - Elsevier
Latin trades are closely related to the problem of critical sets in Latin squares. We denote the
cardinality of the smallest critical set in any Latin square of order n by scs (n). A …
cardinality of the smallest critical set in any Latin square of order n by scs (n). A …
[HTML][HTML] Constructing (0, 1)-matrices with large minimal defining sets
NJ Cavenagh, R Ramadurai - Linear Algebra and its Applications, 2018 - Elsevier
If D is a partially filled-in (0, 1)-matrix with a unique completion to a (0, 1)-matrix M (with
prescribed row and column sums), we say that D is a defining set for M. Let A 2 m, m be the …
prescribed row and column sums), we say that D is a defining set for M. Let A 2 m, m be the …
Critical Sets for Sudoku and General Graphs
J Cooper, A Kirkpatrick - arXiv preprint arXiv:1302.0318, 2013 - arxiv.org
We discuss the problem of finding critical sets in graphs, a concept which has appeared in a
number of guises in the combinatorics and graph theory literature. The case of the Sudoku …
number of guises in the combinatorics and graph theory literature. The case of the Sudoku …