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pro vyhledávání: '"Holt, Derek F"'
We study groups whose co-word problems are ET0L languages, which we call coET0L groups, using an automaton based model due to van Leeuwen, and recently studied by Bishop and Elder. In particular we prove a number of closure results for the class of g
Externí odkaz:
http://arxiv.org/abs/2408.05323
Autor:
Holt, Derek F., Tracey, Gareth
We present a randomised variant of an algorithm of Lucchini and Thakkar for finding a smallest sized generating set in a finite group, which has polynomial time expected running time in finite permutation groups.
Externí odkaz:
http://arxiv.org/abs/2404.03952
Autor:
Holt, Derek F., Rees, Sarah
Our main theorem is that the word problem in the Artin group G = for n >= 5 can be solved using a system R of length preserving rewrite rules that, together with free reduction, can be used to redu
Externí odkaz:
http://arxiv.org/abs/2310.14632
We consider presentations that were derived in \cite{BaumeisterNeaimeRees} for the interval groups associated with proper quasi-Coxeter elements of the Coxeter group $W(D_n)$. We use combinatorial methods to derive alternative presentations for the g
Externí odkaz:
http://arxiv.org/abs/2206.13308
We provide a complete description of the presentations of the interval groups related to quasi-Coxeter elements in finite Coxeter groups. In the simply laced cases, we show that each interval group is the quotient of the Artin group associated with t
Externí odkaz:
http://arxiv.org/abs/2206.09471
We investigate the solution sets to equations in the solvable Baumslag-Solitar groups $BS(1,k)$, $k\geq2$, and show that these sets are represented by EDT0L languages in some cases. In particular, we prove that the multiplication table of such a grou
Externí odkaz:
http://arxiv.org/abs/2204.13758
Publikováno v:
In Journal of Algebra 15 September 2023 630:434-456
Publikováno v:
In Journal of Algebra 1 September 2023 629:399-423