Bean, RichardCavenagh, Nicholas J.2026-09-092026-09-092026Bean, R., & Cavenagh, N. J. (2026). Defining sets which intersect each Latin trade at least twice. Discrete Mathematics, 349(10). https://doi.org/10.1016/j.disc.2026.1152310012-365Xhttps://hdl.handle.net/10289/18631A defining set of a Latin square is a partially filled-in Latin square which completes to no other Latin square of the same order. We introduce the concept of a k -strong defining set, in which if less than k entries are deleted, the property of being a defining set is retained. Equivalently, a k -strong defining set intersects every Latin trade in the Latin square at least k times. In the addition table for integers modulo n , when n is even we determine the minimum size of a k -strong defining set for any k . For odd n we give a construction for a minimally 2-strong defining set. We furthermore give computational results for Latin squares of small orders.enAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/defining setLatin squareLatin trademathematicsmath.COJournal Article10.1016/j.disc.2026.1152314901 Applied Mathematics4904 Pure Mathematics49 Mathematical Sciences4901 Applied mathematics4904 Pure mathematics