# Properties of Cyclic Compositions

## Location

Room 2905 A

## Session Format

Paper Presentation

## Research Area Topic:

Natural & Physical Sciences - Mathematics

## Abstract

A composition of a positive integer 'n' is defined as any sequence of positive integers such that sum to 'n'. Because the order of the parts of a composition matters, compositions arise naturally when storing data efficiently in a fixed amount of space. The number of compositions for 'n' can be enumerated using a formal series called a generating function. This technique can be generalized to consider compositions with restrictions on the parts in the sequence, for instance compositions with modulo constrains on their parts. We consider a specific type of composition called a cyclic composition and give a generating function first enumerating the number of odd parts amongst all cyclic composition of a fixed positive integer. We will examine the various properties of this generating function and consider its relationship to the counting sequences of other combinatorial objects.

## Presentation Type and Release Option

Presentation (Open Access)

## Start Date

4-16-2016 4:00 PM

## End Date

4-16-2016 5:00 PM

## Recommended Citation

Gibson, Moriah, "Properties of Cyclic Compositions" (2016). *GS4 Georgia Southern Student Scholars Symposium*. 76.

https://digitalcommons.georgiasouthern.edu/research_symposium/2016/2016/76

Properties of Cyclic Compositions

Room 2905 A

A composition of a positive integer 'n' is defined as any sequence of positive integers such that sum to 'n'. Because the order of the parts of a composition matters, compositions arise naturally when storing data efficiently in a fixed amount of space. The number of compositions for 'n' can be enumerated using a formal series called a generating function. This technique can be generalized to consider compositions with restrictions on the parts in the sequence, for instance compositions with modulo constrains on their parts. We consider a specific type of composition called a cyclic composition and give a generating function first enumerating the number of odd parts amongst all cyclic composition of a fixed positive integer. We will examine the various properties of this generating function and consider its relationship to the counting sequences of other combinatorial objects.