On the Number of Monochromatic Close Pairs of Beads in a
نویسنده
چکیده
| We consider the following problem: Let r be a n-bead rosary with m white beads and n ? m black beads. Let t be an integer, t n. Denote by MC t (r) the number of pairs, of monochromatic beads which are within distance t apart, in the rosary r. What is the minimum value of MC t (), when the minimum is taken over all n-bead rosaries which consists of m white beads and n ? m black beads? We prove a (reasonably) tight lower bound for this combinatorial problem. Surprisingly, when m = n=2, the answer is (p 2 ? 1) nt, rather than nt=2 that one might have expected.
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