Please use this identifier to cite or link to this item: https://gnanaganga.inflibnet.ac.in:8443/jspui/handle/123456789/7616
Title: A partial Latin squares problen1 posed by Blackburn
Authors: Ian M. Wanless
Issue Date: 2004
Publisher: Bulletin of the Institute of Combinatorics and Its Applications
Abstract: Blackburn asked for the largest possible deusity of fillf:d cells in a pa rtial latiu square with Llw property tha t, whenever t,w > distinct cells Pn.1, and Pci1 are occupied by t.he same symbol the 'opposite corners' P,,,, and Pbc are blank. \Ve show that, as the order n of the partial lat,iu square increases, a density of at least exp (-c(logn) L/'.! ) is possible using a diagonally cyr.lic constmction, where c is a. positive constant. The q uestion of whether a constant density is achievable remains, b ut we show that a density exceeding¼ ( v'fI -1)(1 + 4/ n) is not possible.
URI: http://gnanaganga.inflibnet.ac.in:8080/jspui/handle/123456789/7616
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