Compositions as Non-alternating Sequences of Partitions
نویسندگان
چکیده
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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