Title

Cyclic Permutations of Claps and Pauses

Date

5-30-2013 11:40 AM

Location

Math and Nursing Building (MNB) 104

Department

Mathematics

Session Chair

Hamid Behmard

Session Title

Mathematics Senior Project Presentations 2

Faculty Sponsor(s)

Hamid Behmard

Presentation Type

Symposium

Abstract

In this article we look at different repeated patterns that come from songs. Then remove any indication of different pitches and only look at claps vs. pauses. The question that we are trying to answer is: if we have a combination of claps and pauses, then how many distinct songs can we make? As part of our solution, we allow the repeated pattern to cycle endlessly creating a distinct song. In order to avoid double counting, we use cyclic permutations along with the Burnside's Lemma to find the number of patterns that are fixed and the number of distinct songs.

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May 30th, 11:40 AM

Cyclic Permutations of Claps and Pauses

Math and Nursing Building (MNB) 104

In this article we look at different repeated patterns that come from songs. Then remove any indication of different pitches and only look at claps vs. pauses. The question that we are trying to answer is: if we have a combination of claps and pauses, then how many distinct songs can we make? As part of our solution, we allow the repeated pattern to cycle endlessly creating a distinct song. In order to avoid double counting, we use cyclic permutations along with the Burnside's Lemma to find the number of patterns that are fixed and the number of distinct songs.