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Counting patterns in colored orthogonal arrays

Author
Montejano, A.; Serra, O.
Type of activity
Journal article
Journal
Discrete mathematics
Date of publication
2014-02-28
Volume
317
First page
44
Last page
52
DOI
https://doi.org/10.1016/j.disc.2013.11.002 Open in new window
Project funding
Extremal and optimization problems in graph theory and combinatorics: applications to the analysis and algorithms in communication networks
URL
http://www.sciencedirect.com/science/article/pii/S0012365X13004512 Open in new window
Abstract
Let S be an orthogonal array OA(d, k) and let c be an r-coloring of its ground set X. We give a combinatorial identity which relates the number of vectors in S with given color patterns under c with the cardinalities of the color classes. Several applications of the identity are considered. Among them it is shown that every coloring of an orthogonal array OA(d, d - 1) contains a positive proportion of almost rainbow vectors and also of almost monochromatic vectors of every color. (C) 2013 Elsevi...
Keywords
Colorings, EQUATIONS, MONOCHROMATIC SCHUR TRIPLES, Monochromatic solutions, NUMBER, Orthogonal arrays, RAINBOW ARITHMETIC PROGRESSIONS, Schur triples
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants