TITLE

THE CAUCHY-SCHWARZ INEQUALITY IN CAYLEY GRAPH AND TOURNAMENT STRUCTURES ON FINITE FIELDS

AUTHOR(S)
FOLDES, STEPHAN; MAJOR, LÁSZLÓ
PUB. DATE
January 2014
SOURCE
Miskolc Mathematical Notes;2014, Vol. 15 Issue 1, p153
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The Cayley graph construction provides a natural grid structure on a finite vector space over a field of prime or prime square cardinality, where the characteristic is congruent to 3 modulo 4, in addition to the quadratic residue tournament structure on the prime subfield. Distance from the null vector in the grid graph defines a Manhattan norm. The Hermitian inner product on these spaces over finite fields behaves in some respects similarly to the real and complex case. An analogue of the Cauchy-Schwarz inequality is valid with respect to the Manhattan norm. With respect to the non-transitive order provided by the quadratic residue tournament, an analogue of the Cauchy-Schwarz inequality holds in arbitrarily large neighborhoods of the null vector, when the characteristic is an appropriate large prime.
ACCESSION #
97250463

 

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