Counting Rises, Levels, and Drops in Compositions
نویسندگان
چکیده
A composition of n ∈ N is an ordered collection of one or more positive integers whose sum is n. The number of summands is called the number of parts of the composition. A palindromic composition of n is a composition of n in which the summands are the same in the given or in reverse order. In this paper we study the generating function for the number of compositions (respectively, palindromic compositions) of n with m parts in a given set A ⊆ N with respect to the number of rises, levels, and drops, and obtain previously known results as well as new results. We also generalize results for Carlitz compositions and for partitions. AMS Classification Number: 05A05, 05A15
منابع مشابه
Rises, Levels, Drops and “+” Signs in Compositions: Extensions of a Paper by Alladi and Hoggatt
COMPOSITIONS: EXTENSIONS OF A PAPER BY ALLADI AND HOGGATT S. Heubach Department of Mathematics, California State University Los Angeles 5151 State University Drive, Los Angeles, CA 90032-8204 [email protected] P. Z. Chinn Department of Mathematics, Humboldt State University, Arcata, CA 95521 [email protected] R. P. Grimaldi Department of Mathematics, Rose-Hulman Institute of Techno...
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