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Tournaments and Vandermond's determinant

โœ Scribed by Ira Gessel

Publisher
John Wiley and Sons
Year
1979
Tongue
English
Weight
108 KB
Volume
3
Category
Article
ISSN
0364-9024

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โœฆ Synopsis

We prove that det Ix{-'Inxn =nlsi.=j5n (xi -xi) by associating a tournament to each.term in the expansion of the product. All terms cancel except those corresponding to transitive tournaments, and their sum is the determinant.

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## Abstract Given a tournament __T__, the __tournament game__ on __T__ is as follows: Two players independently pick a node of __T.__ If both pick the same node, the game is tied. Otherwise, the player whose node is at the tail of the arc connecting the two nodes wins. We show that the optimal mixe