Related papers: A presentation for the partial dual inverse symmet…
We show that, for SU(2) generators of arbitrary dimension $D$, there exist identities that express the completely symmetric product of $D$ matrices in terms of completely symmetric products of fewer number of matrices. We also indicate why…
In this paper we study the representation theory of three monoids of partial functions on an $n$-set. The monoid of all order-preserving functions (i.e., functions satisfying $f(x)\leq f(y)$ if $x\leq y$) the monoid of all order-decreasing…
We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…
Every $F$-inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $\sigma$-class. In this enriched signature, the class of all $F$-inverse monoids forms a variety of algebraic…
We introduce a notion of parity for formal morphisms between invertible objects and use it to prove a corresponding coherence theorem. Parity is conceptually similar to the sign of underlying permutations, but not defined as such. To give…
In this thesis we study the subsemigroup structure of the symmetric inverse monoid $I_X$, the inverse semigroup of bijections between subsets of the set $X$, when $X$ is an infinite set. We explore three different approaches to this task.…
Many finite symmetric integral non-representable relation algebras, including almost all Monk algebras, can be embedded in the completion of an atomic symmetric integral representable relation algebra whose finitely-generated subalgebras…
We develop a unified representation theory for the categories of finite subsets and relation-preserving maps of highly homogeneous relational structures classified by Cameron. For any commutative coefficient ring $k$, we extend the…
Green's relations on the deformed finite inverse symmetric semigroup $\mathcal{IS}_n$ and the deformed finite symmetric semigroup $\mathcal{T}_n$ are described.
Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…
We give a finite presentation by generators and relations of the unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOT-dihedral operators. To this end, we introduce a notion of normal form for CNOT-dihedral…
We define homological matrices, construct examples of one-dimension restricted homological quantum field theories, and show a relationship between the two theories.
The interrelations between the inverse problems of the representation theory and the categorical representation theory are discussed.
Combinatorial aspects of multivariate diagonal invariants of the symmetric group are studied. As a consequence it is proved the existence of a multivariate extension of the classical Robinson-Schensted correspondence. Further byproduct are…
Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.
We show how to construct a family of groups with simple commutator subgroups from aperiodic 1-vertex, finitely aligned higher rank graphs (which are, in fact, a class of cancellative monoids). Inverse semigroups form the intermediary…
We extend the theory of fast Fourier transforms on finite groups to finite inverse semigroups. We use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its…
We review several algebraic, combinatorial and geometric interpretations of motivic Donaldson-Thomas invariants of symmetric quivers.
We give a characterisation of the idempotents of the partition monoid, and use this to enumerate the idempotents in the finite partition, Brauer and partial Brauer monoids, giving several formulae and recursions for the number of…
We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of…