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pro vyhledávání: '"MITCHELL, J. D."'
The height of a poset $P$ is the supremum of the cardinalities of chains in $P$. The exact formula for the height of the subgroup lattice of the symmetric group $\mathcal{S}_n$ is known, as is an accurate asymptotic formula for the height of the subs
Externí odkaz:
http://arxiv.org/abs/2310.08229
In this short note, we show that the number of monogenic submonoids of the full transformation monoid of degree $n$ for $n > 0$, equals the sum of the number of cyclic subgroups of the symmetric groups on $1$ to $n$ points. We also prove an analogous
Externí odkaz:
http://arxiv.org/abs/2303.12387
In this paper we consider the questions of which topological semigroups embed topologically into the full transformation monoid $\mathbb{N} ^ \mathbb{N}$ or the symmetric inverse monoid $I_{\mathbb{N}}$ with their respective canonical Polish semigrou
Externí odkaz:
http://arxiv.org/abs/2302.08988
Autor:
Cirpons, R., Mitchell, J. D.
We present efficient computational solutions to the problems of checking equality, performing multiplication, and computing minimal representatives of elements of free bands. A band is any semigroup satisfying the identity $x ^ 2 \approx x$ and the f
Externí odkaz:
http://arxiv.org/abs/2209.05334
In this paper we present general techniques for characterising minimal and maximal semigroup topologies on the endomorphism monoid $\operatorname{End}(\mathbb{A})$ of a countable relational structure $\mathbb{A}$. As applications, we show that the en
Externí odkaz:
http://arxiv.org/abs/2203.11577
In this paper we provide an account of the Todd-Coxeter algorithm for computing congruences on semigroups and monoids. We also give a novel description of an analogue for semigroups of the so-called Felsch strategy from the Todd-Coxeter algorithm for
Externí odkaz:
http://arxiv.org/abs/2203.11148
In this paper, we determine minimal generating sets for several well-known monoids of matrices over semirings. In particular, we find minimal generating sets for the monoids consisting of: all $n\times n$ boolean matrices when $n\leq 8$; the $n\times
Externí odkaz:
http://arxiv.org/abs/2012.10323
In this short note, we describe generating sets for the monoids of consisting of all $2 \times 2$ matrices over certain finite tropical semirings.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/2009.10372
Publikováno v:
Trans. Amer. Math. Soc., Vol. 376, (2023) 8023-8093
In this paper we explore the extent to which the algebraic structure of a monoid $M$ determines the topologies on $M$ that are compatible with its multiplication. Specifically we study the notions of automatic continuity; minimal Hausdorff or Polish
Externí odkaz:
http://arxiv.org/abs/1912.07029