Congruences of Concave Composition Functions
نویسندگان
چکیده
Concave compositions are ordered partitions whose parts are decreasing towards a central part. We study the distribution modulo a of the number of concave compositions. Let c(n) be the number of concave compositions of n having even length. It is easy to see that c(n) is even for all n 1. Refining this fact, we prove that #{n < X : c(n) ⌘ 0 (mod 4)} p X and also that for every a > 2 and at least two distinct values of r 2 {0, 1, . . . , a 1}, #{n < X : c(n) ⌘ r (mod a)} > log2 log3 X a . We obtain similar results for concave compositions of odd length.
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