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Operator Symmetry on Functions

Show simple item record Seule, Khora 2021-08-11T08:05:27Z 2021-08-11T08:05:27Z 2021-04-28
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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