32 citations · 341 across the 33 of their papers we have counts for
37 papers
On right units of special inverse monoids
Igor Dolinka, Robert D. Gray
We study the class of monoids that arise as the submonoid of right units of finitely presented special inverse monoids (SIMs). Gray and Ruškuc (2024) gave the first example of a fi…
Semirigidity and the enumeration of nilpotent semigroups of index three
Igor Dolinka, D. G. FitzGerald, James D. Mitchell
There is strong evidence for the belief that `almost all' finite semigroups, whether we consider multiplication operations on a fixed set or their isomorphism classes, are nilpoten…
Congruences of maximum regular subsemigroups of variants of finite full transformation semigroups
Igor Dolinka, James East, Nik Ruškuc
Let be the full transformation monoid over a finite set , and fix some of rank . The variant has underlying set , and operation .…
Semiring and involution identities of powers of inverse semigroups
Igor Dolinka, Sergey V. Gusev, Mikhail V. Volkov
The set of all subsets of any inverse semigroup forms an involution semiring under set-theoretical union and element-wise multiplication and inversion. We find structural condition…
Prefix monoids of groups and right units of special inverse monoids
Igor Dolinka, Robert D. Gray
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,…
Product decompositions of semigroups induced by action pairs
Scott Carson, Igor Dolinka, James East +2
This paper concerns a class of semigroups that arise as products , associated to what we call `action pairs'. Here and are subsemigroups of a common monoid and, roughly…
Elaborating the word problem for free idempotent-generated semigroups over the full transformation monoid
Igor Dolinka
With each semigroup one can associate a partial algebra, called the biordered set, which captures important algebraic and geometric features of the structure of idempotents of that…
Free idempotent generated semigroups: The word problem and structure via gain graphs
Igor Dolinka
Building on the previous extensive study of Yang, Gould and the present author, we provide a more precise insight into the group-theoretical ramifications of the word problem for f…
New results on the prefix membership problem for one-relator groups
Igor Dolinka, Robert D. Gray
In this paper we prove several results regarding decidability of the membership problem for certain submonoids in amalgamated free products and HNN extensions of groups. These gene…
Sandwich semigroups in diagram categories
Ivana Đurđev, Igor Dolinka, James East
This paper concerns a number of diagram categories, namely the partition, planar partition, Brauer, partial Brauer, Motzkin and Temperley-Lieb categories. If denotes a…
A group-theoretical interpretation of the word problem for free idempotent generated semigroups
Yang Dandan, Igor Dolinka, Victoria Gould
The set of idempotents of any semigroup carries the structure of a biordered set, which contains a great deal of information concerning the idempotent generated subsemigroup of the…
Sandwich semigroups in locally small categories II: Transformations
Igor Dolinka, Ivana Ðurđev, James East +4
Fix sets and , and write for the set of all partial functions . Fix a partial function , and define the operation on $\mathca…
Sandwich semigroups in locally small categories I: Foundations
Igor Dolinka, Ivana Đurđev, James East +4
Fix (not necessarily distinct) objects and of a locally small category , and write for the set of all morphisms . Fix a morphism , and defi…
Universal locally finite maximally homogeneous semigroups and inverse semigroups
Igor Dolinka, Robert D. Gray
In 1959, P. Hall introduced the locally finite group , today known as Hall's universal group. This group is countable, universal, simple, and any two finite isomorphic…
Presentations for singular wreath products
Ying-Ying Feng, Asawer Al-Aadhami, Igor Dolinka +2
For a monoid and a subsemigroup of the full transformation semigroup , the wreath product is defined to be the semidirect product , with the coo…
The idempotent generated subsemigroup of the Kauffman monoid
Igor Dolinka, James East
We characterise the elements of the (maximum) idempotent generated subsemigroup of the Kauffman monoid in terms of combinatorial data associated to certain normal forms. We also ca…
Motzkin monoids and partial Brauer monoids
Igor Dolinka, James East, Robert D. Gray
We study the partial Brauer monoid and its planar submonoid, the Motzkin monoid. We conduct a thorough investigation of the structure of both monoids, providing information on norm…
Twisted Brauer monoids
Igor Dolinka, James East
We investigate the structure of the twisted Brauer monoid , comparing and contrasting it to the structure of the (untwisted) Brauer monoid . We charac…
Finite bands are finitely related
Igor Dolinka
We prove that every finite idempotent semigroup (band) is finitely related, which means that the clone of its term operations (i.e. operations induced by words) is determined by fi…
Enumeration of idempotents in planar diagram monoids
Igor Dolinka, James East, Athanasios Evangelou +5
We classify and enumerate the idempotents in several planar diagram monoids: namely, the Motzkin, Jones (a.k.a. Temperley-Lieb) and Kauffman monoids. The classification is in terms…
Idempotent rank in the endomorphism monoid of a non-uniform partition
Igor Dolinka, James East, James D. Mitchell
We calculate the rank and idempotent rank of the semigroup generated by the idempotents of the semigroup , which consists of all transformations of the finite set…
Semigroups of rectangular matrices under a sandwich operation
Igor Dolinka, James East
Let denote the set of all matrices over a field , and fix some matrix . An asso…
On regularity and the word problem for free idempotent generated semigroups
Igor Dolinka, Robert D. Gray, Nik Ruškuc
The category of all idempotent generated semigroups with a prescribed structure of their idempotents (called the biordered set) has an initial object called the f…
Variants of finite full transformation semigroups
Igor Dolinka, James East
The variant of a semigroup S with respect to an element a in S, denoted S^a, is the semigroup with underlying set S and operation * defined by x*y=xay for x,y in S. In this article…