6 papers
The Hesselink stratification of nullcones and base change
Matthew C. Clarke, Alexander Premet
Let be a connected reductive algebraic group over an algebraically closed field of characteristic . We give a case-free proof of Lusztig's conjectures [Unipotent eleme…
On the algebra structure of some bismash products
Matthew C. Clarke
We study several families of semisimple Hopf algebras, arising as bismash products, which are constructed from finite groups with a certain specified factorization. First we associ…
On the endomorphism algebra of generalised Gelfand-Graev representations
Matthew C. Clarke
Let be a connected reductive algebraic group defined over the finite field $\F_q$, where is a power of a good prime for , and let denote the corresponding Frobenius…
Computing nilpotent and unipotent canonical forms: a symmetric approach
Matthew C. Clarke
Let be an algebraically closed field of any characteristic except 2, and let $G = \GL_n(k)$ be the general linear group, regarded as an algebraic group over . Using an algeb…
On the Chances of Completing the Game of "Perpetual Motion"
Matthew C. Clarke
This brief paper describes the single-player card game called "Perpetual Motion" and reports on a computational analysis of the game's outcome. The analysis follows a Monte Carlo m…
Periodic unique beta-expansions: the Sharkovskii ordering
Jean-Paul Allouche, Matthew Clarke, Nikita Sidorov
Let . Each can be represented in the form \[ x=\sum_{k=1}^\infty ε_kβ^{-k}, \] where for all (a -expansion of ). If $β>…