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New Results On Cyclic Compositions And Multicompositions, Silvana Ramaj
New Results On Cyclic Compositions And Multicompositions, Silvana Ramaj
Electronic Theses and Dissertations
Integer compositions, cyclic compositions, and lately k-compositions, are an important topic in combinatorics and number theory. In this paper, we will explain, the general approach of using generating functions to study number sequences involving compositions, cyclic compositions, k-compositions, and the number of parts in each of them. After generating the data, some properties are observed and proved. Also, some interesting bijections involving Pell numbers and the Jacobsthal sequence are given.
Combinatorics Of Compositions, Meghann M. Gibson
Combinatorics Of Compositions, Meghann M. Gibson
Electronic Theses and Dissertations
Integer compositions and related enumeration problems have been extensively studied. The cyclic analogues of such questions, however, have significantly fewer results. In this thesis, we follow the cyclic construction of Flajolet and Soria to obtain generating functions for cyclic compositions and n-color cyclic compositions with various restrictions. With these generating functions we present some statistics and asymptotic formulas for the number of compositions and parts in such compositions. Combinatorial explanations are also provided for many of the enumerative observations presented.