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Full-Text Articles in Mathematics
Cycle Structures Of Orthomorphisms Extending Partial Orthomorphisms Of Boolean Groups, Nichole Louise Schimanski, John S. Caughman Iv
Cycle Structures Of Orthomorphisms Extending Partial Orthomorphisms Of Boolean Groups, Nichole Louise Schimanski, John S. Caughman Iv
Mathematics and Statistics Faculty Publications and Presentations
A partial orthomorphism of a group GG (with additive notation) is an injection π:S→G for some S⊆G such that π(x)−x ≠ π(y) for all distinct x,y∈S. We refer to |S| as the size of π, and if S=G, then π is an orthomorphism. Despite receiving a fair amount of attention in the research literature, many basic questions remain concerning the number of orthomorphisms of a given group, and what cycle types these permutations have.
It is known that conjugation by automorphisms of G forms a group action on the set of orthomorphisms of G. In this paper, we consider the …
Math And Sudoku: Exploring Sudoku Boards Through Graph Theory, Group Theory, And Combinatorics, Kyle Oddson
Math And Sudoku: Exploring Sudoku Boards Through Graph Theory, Group Theory, And Combinatorics, Kyle Oddson
Student Research Symposium
Encoding Sudoku puzzles as partially colored graphs, we state and prove Akman’s theorem [1] regarding the associated partial chromatic polynomial [5]; we count the 4x4 sudoku boards, in total and fundamentally distinct; we count the diagonally distinct 4x4 sudoku boards; and we classify and enumerate the different structure types of 4x4 boards.