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# Operator Symmetry on Functions

 dc.contributor.author Seule, Khora dc.date.accessioned 2021-08-11T08:05:27Z dc.date.available 2021-08-11T08:05:27Z dc.date.issued 2021-04-28 dc.identifier.uri https://jewlscholar.mtsu.edu/handle/mtsu/6547 dc.description.abstract All functions possess symmetries over their input with certain operators. So-called Symmetry-Sets over a given function and operator are the sets of objects that can be operated with the input to the function under that operator without effecting the output of the function. This work shows that when the domain of a function forms algebraic structure – e.g. a Monoid, Group, Ring, etc. – with a given operator or pair of operators, the Symmetry-Sets over the same operator(s) have many nice properties. The work develops and enumerates many interesting results on so-called Tessellations – functions from the integers to some at-least cancellative-algebra – using the structure of Symmetry-Sets on them, i.e. Period-Sets when speaking of Tessellations. The behavior of the principal period of any given Tesselation is detailed, as well as how they interact with each-other when Tesselations are operated together using generalized function-operators. Briefly, a venue is developed for studying these Symmetry-Sets more thoroughly, by introducing the notion of Allgebras, an element set paired with the set of all definable operators on the element set. In this context, algebraic structures are relations between subsets of elements and operators. en_US dc.language.iso en_US en_US dc.publisher University Honors College Middle Tennessee State University en_US dc.subject Computer of Basic and Applied Sciences en_US dc.subject Abstract Algebra en_US dc.subject Functions en_US dc.subject Rings en_US dc.subject principal ideal domain en_US dc.subject PID en_US dc.subject Integers en_US dc.subject alternative set theory en_US dc.title Operator Symmetry on Functions en_US dc.type Thesis en_US
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