COMPOSITIONS OF n WITH PARTS IN A SET
نویسندگان
چکیده
Let A be any set of positive integers and n ∈ N. A composition of n with parts in A is an ordered collection of one or more elements in A whose sum is n. A palindromic composition of n with parts in A is a composition of n with parts in A in which the summands are the same in the given or in reverse order. A Carlitz (palindromic) composition of n with parts in A is a (palindromic) composition of n with parts in A in which no adjacent parts are the same. In this paper, we study the generating functions for several counting problems for compositions, palindromic compositions, Carlitz compositions, and Carlitz palindromic compositions with parts in A, respectively. Our theorems contain many previously known results as special cases, as well as many new results. We also prove some of our results using direct counting arguments. AMS Classification Number: 05A05, 05A15
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