Hecke–Rogers, Andrews identities; combinatorial proofs
نویسندگان
چکیده
منابع مشابه
Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao
We revisit a classic partition theorem due to MacMahon that relates partitions with all parts repeated at least once and partitions with parts congruent to 2, 3, 4, 6 (mod 6), together with a generalization by Andrews and two others by Subbarao. Then we develop a unified bijective proof for all four theorems involved, and obtain a natural further generalization as a result.
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Brualdi and Ma found a connection between involutions of length n with k descents and symmetric k×k matrices with non-negative integer entries summing to n and having no row or column of zeros. From their main theorem they derived two alternating sums by algebraic means and asked for combinatorial proofs. The purpose of this note is to give such demonstrations.
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We provide combinatorial proofs of six of the ten q-series identities listed in [3, Theorem 3]. Andrews, Jiménez-Urroz and Ono prove these identities using formal manipulation of identities arising in the theory of basic hypergeometric series. Our proofs are purely combinatorial, based on interpreting both sides of the identities as generating functions for certain partitions. One of these iden...
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This paper focuses on two binomial identities. The proofs illustrate the power and elegance in enumerative/algebraic combinatorial arguments, modern machineassisted techniques of Wilf-Zeilberger and the classical tools of generatingfunctionology.
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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 ca...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90131-z