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Full-Text Articles in Algebra
Gray Codes In Music Theory, Isaac L. Vaccaro
Gray Codes In Music Theory, Isaac L. Vaccaro
Electronic Theses and Dissertations
In the branch of Western music theory called serialism, it is desirable to construct chord progressions that use each chord in a chosen set exactly once. We view this problem through the scope of the mathematical theory of Gray codes, the notion of ordering a finite set X so that adjacent elements are related by an element of some specified set R of involutions in the permutation group of X. Using some basic results from the theory of permutation groups we translate the problem of finding Gray codes into the problem of finding Hamiltonian paths and cycles in a Schreier …
Connectedness In Cayley Graphs And P/Np Dichotomy For Quay Algebras, Thuy Trang Nguyen
Connectedness In Cayley Graphs And P/Np Dichotomy For Quay Algebras, Thuy Trang Nguyen
Senior Projects Spring 2020
This senior thesis attempts to determine the extent to which the P/NP dichotomy of finite algebras (as proven by Bulatov, et.al in 2017) can be cast in terms of connectedness in Cayley graphs. This research is motivated by Prof. Robert McGrail's work ``CSPs and Connectedness: P/NP-Complete Dichotomy for Idempotent, Right Quasigroups" published in 2014 in which he demonstrates the strong correspondence between tractability and total path-connectivity in Cayley graphs for right, idempotent quasigroups. In particular, we will introduce the notion of total V-connectedness and show how it could be potentially used to phrase the dichotomy in terms of connectivity for …