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Full-Text Articles in Number Theory
On The Order-Type Complexity Of Words, And Greedy Sidon Sets For Linear Forms, Yin Choi Cheng
On The Order-Type Complexity Of Words, And Greedy Sidon Sets For Linear Forms, Yin Choi Cheng
Dissertations, Theses, and Capstone Projects
This work consists of two parts. In the first part, we study the order-type complexity of right-infinite words over a finite alphabet, which is defined to be the order types of the set of shifts of said words in lexicographical order. The set of shifts of any aperiodic morphic words whose first letter in the purely-morphic pre-image occurs at least twice in the pre-image has the same order type as Q ∩ (0, 1), Q ∩ (0, 1], or Q ∩ [0, 1). This includes all aperiodic purely-morphic binary words. The order types of uniform-morphic ternary words were also studied, …