Combinatorial proofs of Andrews’ formulas on concave compositions
نویسنده
چکیده
Concave compositions were recently introduced by Andrews[3] in the study of orthogonal polynomials, see also Andrews [4]. A concave composition of even length 2m, is a sum of the form ∑ ai + ∑ bi such that a1 > a2 > · · · > am = bm < bm−1 < · · · < b1, where am ≥ 0, and all ai and bi are integers. Let CE(n) denote the set of concave compositions of even length that sum to n, and ce(n) be the cardinality of CE(n). By an analytic tool, Andrews derived the generating function of ce(n) as follows.
منابع مشابه
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