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.
Author Rights: Apply an Embargo
4-22-2016
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.
