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On chromatic numbers of space-times: open problems
Chromatic number: reminder. A chromatic number χ(S) of a metric space S is defined as the smallest number of colors in a coloring of S in which no two points of the same color are unit distance apart; see, e.g., (Soifer 2009) and references therein. Space-times: reminder. What will happen if we define a similar quantity for space-times, e.g., for pseudo-Euclidean (Minkowski) spaces R 1,n in whi...
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1. Notation. Let Z and N be the sets of integers and positive integers respectively. For b, c ∈ Z the Lucas sequences {U n (b, c)} and {V n (b, c)} are defined by (1.1) U 0 (b, c) = 0, U 1 (b, c) = 1, U n+1 (b, c) = bU n (b, c) − cU n−1 (b, c) (n ≥ 1) and (1.2) V 0 (b, c) = 2, V 1 (b, c) = b, V n+1 (b, c) = bV n (b, c) − cV n−1 (b, c) (n ≥ 1). Let d = b 2 − 4c. It is well known that for n ∈ N, ...
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