Cavenagh, Nicholas J.Wanless, Ian M.2017-08-3120162017-08-312016Cavenagh, N. J., & Wanless, I. M. (2016). There are asymptotically the same number of Latin squares of each parity. Bulletin of the Australian Mathematical Society, 94(2), 187–194. https://doi.org/10.1017/S00049727160001740004-9727https://hdl.handle.net/10289/11296A Latin square is reduced if its first row and column are in natural order. For Latin squares of a particular order n there are four possible different parities. We confirm a conjecture of Stones and Wanless by showing asymptotic equality between the numbers of reduced Latin squares of each possible parity as the order n → ∞.application/pdfenThis is an author’s accepted version of an article published in the journal: Bulletin of the Australian Mathematical Society. © 2016 Australian Mathematical Publishing Association Inc.Science & TechnologyPhysical SciencesMathematicsLatin squareparityAlon-Tarsi conjecturerow cycleALON-TARSI CONJECTUREJournal Article10.1017/S00049727160001741755-1633