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DESCRIPTION: An n×n array with entries in [n] such that each integer appear
s exactly once in every row and every column is called a Latin square of o
rder n . Two Latin squares L and L' are said to be orthogonal if\, for al
l x\,y∈[n]\, there is a unique pair (i\,j) such that L(i\,j) = x and L'(i\,
j) = y\; k Latin squares are mutually orthogonal if any two of them are o
rthogonal. After the question of existence of a combinatorial structure sa
tisfying given properties\, a natural and important problem is to determine
how many such objects there are. In this talk\, we will consider some coun
ting questions related to (mutually) orthogonal Latin squares. We will pres
ent an upper bound on the number of ways to extend a set of k mutually orth
ogonal Latin squares to a set of k+1 mutually orthogonal Latin squares and
discuss some applications\, comparing the resulting bounds to previously kn
own lower and upper bounds. This talk is based on joint work with Shagnik D
as and Tibor Szabó.
DTSTAMP:20190607T132700
DTSTART:20190624T160000
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Simona Boyadzhiyska (Freie Universität Berlin): On counting problem
s related to (mutually) orthogonal Latin squares
UID:95691164@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20190624-C-Boyadzhiyska.html
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