arXiv subjects

Preechaya Sanyatit

Publications and source records attributed to Preechaya Sanyatit.

2 recordsLinked to original sources

arXiv2023

Union vertex-distinguishing edge colorings

The union vertex-distinguishing chromatic index $χ'_\cup(G)$ of a graph $G$ is the smallest natural number $k$ such that the edges of $G$ can be assigned nonempty subsets of $[k]$ so that the union of the subsets assigned to the edges incident to each vertex is different. We prove that $χ'_\cup(G) \in \left\{ \left\lceil \log_2\left(n +1\right) \right\rceil, \left\lceil \log_2\left(n +1\right) \right\rceil+1 \right\}$ for a graph $G$ on $n$ vertices without a component of order at most two. This answers a question posed by Bousquet, Dailly, Duchêne, Kheddouci and Parreau, and independently by Chartrand, Hallas and Zhang.

math.CO↗

arXiv2019

Isomorphism of uniform algebras on the 2-torus

For $α$ a positive irrational, let $\mathcal{A}_α$ be the subalgebra of continuous functions on the two-torus whose Fourier transform vanishes at $(m, n)$ if $m + αn < 0.$ These algebras were studied by Wermer and others, who proved properties such as maximality and characterized the Gelfand space. One of the major themes of current work in operator algebras is classification, but none of the properties which were investigated earlier distinguished between $\mathcal{A}_α$ and $\mathcal{A}_β,$ if $β$ is another positive irrational. We address this question. We also determine the automorphism group of $\mathcal{A}_α.$

math.FA↗