5 papers · 1 filter
Information and Locality in Cayley Graphs
Ming-Hsuan Kang, Yu-Hsuan Hsieh
A de Bruijn sequence is the cyclic prototype of a Cayley-graph observation problem: when does the ordered label word on a translated window determine the vertex ? We distin…
Universal Cycles for Affine Planes and 3-Subspaces over Finite Fields
Yu Hsuan Hsieh, Ming-Hsuan Kang
We construct universal cycles for affine planes in for all prime powers and all , using sliding windows of length three. The construction is local-to-glo…
Universal Cycles on Affine Lines
Ming-Hsuan Kang, Shin-Hsun Chou
A universal cycle is a cyclic sequence in which each object of a combinatorial family appears exactly once as a contiguous window. While such cycles are well understood for many di…
Algebraic Constructions of Universal Cycles on Grassmannians G_q(2,n)
Chen Yu Chi, Ming Hsuan Kang, Yu Hsuan Hsieh
We study universal cycles on the Grassmannian , the set of -dimensional -subspaces of . While their existence is known from inductive and…
De Bruijn Tori Without Zeros: A Field-Theoretic Perspective
Ming Hsuan Kang, Yu Hsuan Hsieh
We present an algebraic construction of trace-based De Bruijn tori over finite fields, focusing on the nonzero variant that omits the all-zero pattern. The construction arranges no…