Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651364 | Discrete Mathematics | 2006 | 14 Pages |
Abstract
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)scs(n). A consideration of Latin trades which consist of just two columns, two rows, or two elements establishes that scs(n)⩾n-1scs(n)⩾n-1. We conjecture that a consideration of Latin trades on four rows may establish that scs(n)⩾2n-4scs(n)⩾2n-4. We look at various attempts to prove a conjecture of Cavenagh about such trades. The conjecture is proven computationally for values of n less than or equal to 9. In particular, we look at Latin squares based on the group table of ZnZn for small n and trades in three consecutive rows of such Latin squares.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Richard Bean,