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pro vyhledávání: '"Gray, Robert D."'
Autor:
Gray, Robert D., Steinberg, Benjamin
Publikováno v:
Comptes Rendus. Mathématique, Vol 359, Iss 8, Pp 1047-1057 (2021)
We give a topological proof that a free inverse monoid on one or more generators is neither of type left-$\mathrm{FP}_2$ nor right-$\mathrm{FP}_2$. This strengthens a classical result of Schein that such monoids are not finitely presented as monoids.
Externí odkaz:
https://doaj.org/article/1d7b20fa6a46479b92395d10ba973b4a
We study several natural decision problems in braid groups and Artin groups. We classify the Artin groups with decidable submonoid membership problem in terms of the non-existence of certain forbidden induced subgraphs of the defining graph. Furtherm
Externí odkaz:
http://arxiv.org/abs/2409.11335
The purpose of this paper is to introduce a new family of semigroups - the free projection-generated regular $*$-semigroups - and initiate their systematic study. Such a semigroup $PG(P)$ is constructed from a projection algebra $P$, using the recent
Externí odkaz:
http://arxiv.org/abs/2406.09109
Autor:
Gray, Robert D., Kambites, Mark
We continue the study of the structure of general subgroups (in particular maximal subgroups, also known as group $\mathcal{H}$-classes) of special inverse monoids. Recent research of the authors has established that these can be quite wild, but in t
Externí odkaz:
http://arxiv.org/abs/2306.17787
Motivated by approaches to the word problem for one-relation monoids arising from work of Adian and Oganesian (1987), Guba (1997), and Ivanov, Margolis and Meakin (2001), we study the submonoid and rational subset membership problems in one-relation
Externí odkaz:
http://arxiv.org/abs/2305.15672
Autor:
Dolinka, Igor, Gray, Robert D.
A prefix monoid is a finitely generated submonoid of a finitely presented group generated by the prefixes of its defining relators. Important results of Guba (1997), and of Ivanov, Margolis and Meakin (2001), show how the word problem for certain one
Externí odkaz:
http://arxiv.org/abs/2304.08084
Autor:
Gray, Robert D., Kambites, Mark
We study the maximal subgroups (also known as group $\mathcal{H}$-classes) of finitely presented special inverse monoids. We show that the maximal subgroups which can arise in such monoids are exactly the recursively presented groups, and moreover ev
Externí odkaz:
http://arxiv.org/abs/2212.04204
Autor:
Gray, Robert D., Ruskuc, Nik
We investigate the groups of units of one-relator and special inverse monoids. These are inverse monoids which are defined by presentations where all the defining relations are of the form $r=1$. We develop new approaches for finding presentations fo
Externí odkaz:
http://arxiv.org/abs/2103.02995
Autor:
East, James, Gray, Robert D.
This article concerns Ehresmann structures in the partition monoid $P_X$. Since $P_X$ contains the symmetric and dual symmetric inverse monoids on the same base set $X$, it naturally contains the semilattices of idempotents of both submonoids. We sho
Externí odkaz:
http://arxiv.org/abs/2011.00663
Autor:
Gray, Robert D., Steinberg, Benjamin
We give a topological proof that a free inverse monoid on one or more generators is neither of type left-$FP_2$ nor right-$FP_2$. This strengthens a classical result of Schein that such monoids are not finitely presented as monoids.
Comment: 5 p
Comment: 5 p
Externí odkaz:
http://arxiv.org/abs/2002.07690