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.
