✦ LIBER ✦

Simple product colorings

✍ Scribed by Peter D Johnson Jr.

Publisher: Elsevier Science
Year: 1984
Tongue: English
Weight: 131 KB
Volume: 48
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90133-x

No coin nor oath required. For personal study only.

✦ Synopsis

If A is a set colored with m colors, and B is colored with n colors, the coloring of A x B obtained by coloring (a, b) with the pair (color of a, color of b) will be called an m x n simple product coloring (SPC) of A x B. SPC's of Cartesian products of three or more sets are defined analogously. It is shown that there are 2 x 2, and 2 x 2 x 2 SPC's of Q2 and Q3 which forbid the distance one; that there is no 2 k SPC of Qk forbidding the distance one, for k>3; and that there is no 2 x 2 SPC of O x O(x/~), and thus none of R2, forbidding the distance 1.

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