Compositions as non-alternating sequences of partitions | Zendy

Aubrey Blecher | Zendy; Charlotte Brennan | Zendy; Toufik Mansour | Zendy

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Compositions as non-alternating sequences of partitions

Author(s) -

Aubrey Blecher,

Charlotte Brennan,

Toufik Mansour

Publication year - 2013

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm130515008b

Subject(s) - mathematics , partition (number theory) , combinatorics , generating function , composition (language) , block (permutation group theory) , function (biology) , discrete mathematics , philosophy , linguistics , evolutionary biology , biology

Compositions are conceptualized as non alternating sequences of blocks of non-decreasing and strictly decreasing partitions. We find the generating function F(x; y; q) where x marks the size of the composition, y the number of parts and q the number of such partition blocks minus 1. We form these blocks starting on the left-hand-side of the composition and maximizing the size of each block. We also find the generating function for the total number of such blocks.

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