Inverse monoids of partial graph automorphisms

关于幂幺半群及其自同构

On power monoids and their automorphisms

本文研究包含0的自然数有限子集在集合加法下构成的幺半群，证明其唯一非平凡自同构为取最大值后反射的对合，证明基于加性数论与箱维数归纳。

Enumerating kth Roots in the Symmetric Inverse Monoid

The symmetric inverse monoid, SIM(n), is the set of all partial one-to-one mappings from the set {1, 2, ... , n} to itself under the operation of composition. Earlier research on the symmetric inverse monoid delineated the process for determining whether an element of SIM(n) has a kth root. The problem of enumerating kth roots of a given element of SIM(n) has since been posed, which is solved in this work. In order to find the number of kth roots of an element, all that is needed is to know the cycle and path structure of the element. Conveniently, the cycle and cycle-free components may be co…

A presentation for the partial dual inverse symmetric monoid

We give a monoid presentation in terms of generators and defining relations for the partial analogue of the finite dual inverse symmetric monoid.

Ramified inverse and planar monoids

Ramified monoids are a class of monoids introduced by the authors. The main motivation for considering these monoids comes from knot theory, see [3, 4, 5]. Thus, in [2] we have studied the ramified monoids of the symmeytric group and of the Brauer monoid, among others. This paper study the ramified of the inverse symmetric monoid, which plays a notable role in knot theory as well, see [10]. Here is also introduced the notion of planar ramified monoid. In particular, we give presentations for some planar ramified monoids arising from noncrossing set partitions.

对“车 rook 幺半群的子半群”一文的扩展

An extension to "A subsemigroup of the rook monoid"

本文扩展了关于车幺半群逆子幺半群的研究，将三元组从整数域推广到实数域，构造新的逆幺半群并证明其具有多种代数性质。

Permutation monoids and MB-homogeneity for graphs and relational structures

In this paper, we investigate the connection between infinite permutation monoids and bimorphism monoids of first-order structures. Taking our lead from the study of automorphism groups of structures as infinite permutation groups and the more recent developments in the field of homomorphism-homogeneous structures, we establish a series of results that underline this connection. Of particular interest is the idea of MB-homogeneity; a relational structure $\mathcal{M}$ is MB-homogeneous if every monomorphism between finite substructures of $\mathcal{M}$ extends to a bimorphism of $\mathcal{M}$.…

The Stylic Monoid

The free monoid $A^*$ on a finite totally ordered alphabet $A$ acts at the left on columns, by Schensted left insertion. This defines a finite monoid, denoted $Styl(A)$ and called the stylic monoid. It is canonically a quotient of the plactic monoid. Main results are: the cardinality of $Styl(A)$ is equal to the number of partitions of a set on $|A|+1$ elements. We give a bijection with so-called $N$-tableaux, similar to Schensted's algorithm, explaining this fact. Presentation of $Styl(A)$: it is generated by $A$ subject to the plactic (Knuth) relations and the idempotent relations $a^2=a$, $…

All reducts of the random graph are model-complete

We study locally closed transformation monoids which contain the automorphism group of the random graph. We show that such a transformation monoid is locally generated by the permutations in the monoid, or contains a constant operation, or contains an operation that maps the random graph injectively to an induced subgraph which is a clique or an independent set. As a corollary, our techniques yield a new proof of Simon Thomas' classification of the five closed supergroups of the automorphism group of the random graph; our proof uses different Ramsey-theoretic tools than the one given by Thomas…

Partial mirror symmetry I: reflection monoids

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders.

Partial symmetry, reflection monoids and Coxeter groups

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders.

Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph

We establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph $R$. As a consequence we show that, for any countable graph $Γ$, there are uncountably many maximal subgroups of the endomorphism monoid of $R$ isomorphic to the automorphism group of $Γ$. Further structural information about End $R$ is established including that Aut $Γ$ arises in uncountably many ways as a Schützenberger group. Similar results are proved for the countable universal directed graph and the countable universal bipartite graph.

Multiple and inverse topplings in the Abelian Sandpile Model

The Abelian Sandpile Model is a cellular automaton whose discrete dynamics reaches an out-of-equilibrium steady state resembling avalanches in piles of sand. The fundamental moves defining the dynamics are encoded by the toppling rules. The transition monoid corresponding to this dynamics in the set of stable configurations is abelian, a property which seems at the basis of our understanding of the model. By including also antitoppling rules, we introduce and investigate a larger monoid, which is not abelian anymore. We prove a number of algebraic properties of this monoid, and describe their …