Presentation Title

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

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Apr 16th, 4:00 PM Apr 16th, 5:00 PM

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.