36 citations · 122 across the 19 of their papers we have counts for
6 papers · 1 filter
A counting proof for the smallest critical set in a Latin square
Richard Bean
A critical set in a Latin square is a set of entries that determines the square uniquely and is minimal with this property. We prove that every partial Latin square of order wi…
A tight single-change covering design with block size 6
Richard Bean
We give a tight single-change covering design with and . This answers Problem 1 of the Nineteenth British Combinatorial Conference, which asked whether such a design ex…
Critical Sets in Latin Squares and Associated Structures
Richard Winston Bean
A critical set in a Latin square of order is a set of entries in an array which can be embedded in precisely one Latin square of order , with the property that i…
Critical sets in the elementary abelian 2- and 3- groups
Richard Bean
In 1998, Khodkar showed that the minimal critical set in the Latin square corresponding to the elementary abelian 2-group of order 16 is of size at most 124. Since the paper was pu…
The size of the smallest uniquely completable set in order 8 Latin squares
Richard Bean
In 1990, Kolesova, Lam and Thiel determined the 283,657 main classes of Latin squares of order 8. Using techniques to determine relevant Latin trades and integer programming, we ex…
A new bound on the size of the largest critical set in a Latin square
Richard Bean, E. S. Mahmoodian
A critical set in an n x n array is a set C of given entries, such that there exists a unique extension of C to an n x n Latin square and no proper subset of C has this property. T…