We study the transcendence of the limit $h(A)$ of the sequence \[A, A^A, A^{A^A},\ldots.\] In 2010, Sondow and Marques studied the case that $A$ is rational numbers or algebraic numbers satisfying some special conditions. In this talk, we extend their results and give an asymptotic formula for the number of algebraic numbers $A$ such that $h(A)$ is algebraic. This is the joint work with Hirotaka Kobayashi and Kota Saito. Google meet link for this talk is meet.google.com/yvz-yngc-nif

Webinar: join at https://meet.google.com/bbj-oeri-ccz It is known that Vertex Cover is polynomial time solvable in the class of chordal graphs. We consider this problem in a graph that has at most $k$ vertices whose deletion results in a chordal graph, when parameterized by $k$. While this investigation fits naturally into the recent trend of what are called 'structural parameterizations', here we assume that the deletion set is not given. Specifically, we show a $2^{O(k)}n^{O(1)}$ time algorithm for Vertex Cover parameterized by the size of chordal vertex deletion set when the chordal deletion set is not given as a part of the input.

TBA