## Biography

Janusz Konieczny, Professor of Mathematics, earned a Ph.D. (1992) in mathematics from Pennsylvania State University, after receiving an M.S. (1982) in computer science and an M.S. (1978) in mathematics from Jagiellonian University (Poland). Among his honors is the UMW Alumni Association Outstanding Young Faculty Member Award and Waple Faculty Professional Achievement Award. He is the author of over 50 research articles in the theory of algebraic semigroups. His most recent articles have appeared in International Journal of Group Theory, Communications in Algebra, Semigroup Forum, and Journal of Algebra. Recently, he has given a presentation at the meeting of the American Mathematical Society. Dr. Konieczny was awarded a Waple Professorship for 2015-2017 and a sabbatical leave for the fall of 2017.

## Areas of Expertise (2)

### Philosophy of Mathematics

### Abstract Algebra

## Accomplishments (2)

#### Mary Washington Faculty Development Grant (professional)

2011-01-01

Awarded by the University of Mary Washington.

#### Alumni Association Outstanding Young Faculty Member Award (professional)

1996-01-01

Awarded by the University of Mary Washington Alumni Association.

## Education (3)

#### Pennsylvania State University: Ph.D., Mathematics 1992

#### Jagiellonian University: M.S., Computer Science 1982

#### Jagiellonian University: M.S., Mathematics 1978

## Links (1)

## Event Appearances (1)

#### The Commuting Graph of the Symmetric Inverse Semigroup

**Analysis, Logic and Physics Seminar** Richmond, VA

2013-09-27

## Articles (5)

#### The commuting graph of the symmetric inverse semigroup

*Israel Journal of Mathematics*

2015-04-01

The goal of this paper is to begin the study of the commuting graph of the symmetric inverse semigroup I(X). We calculate the clique number of G(I(X)), the diameters of the commuting graphs of the proper ideals of I(X), and the diameter of G(I(X)) when |X| is even or a power of an odd prime. We show that when |X| is odd and divisible by at least two primes, then the diameter of G(I(X)) is either 4 or 5.

#### The largest subsemilattices of the endomorphism monoid of an independence algebra

*Linear Algebra and its Applications*

2014-10-01

We prove that a largest subsemilattice of End(A) has either 2n−1 elements (if the clone of A does not contain any constant operations) or 2n elements (if the clone of A contains constant operations). As corollaries, we obtain formulas for the size of the largest subsemilattices of: some variants of the monoid of linear operators of a finite-dimensional vector space, the monoid of full transformations on a finite set X, the monoid of partial transformations on X, the monoid of endomorphisms of a free G-set with a finite set of free generators, among others.

#### Automorphism groups of endomorphism monoids of free G-sets

*Asian-European Journal of Mathematics*

2014-03-01

Let G be a group. A G-set is a nonempty set A together with a (right) action of G on A. The class of G-sets, viewed as unary algebras, is a variety. For a set X, let AG(X) be the free algebra on X in the variety of G-sets. We determine the group of automorphisms of End(AG(X)), the monoid of endomorphisms of AG(X).

#### Conjugation in semigroups

*Journal of Algebra*

2014-02-01

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing definitions, characterize the conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups when the set is infinite.

#### Centralizers in the infinite symmetric inverse semigroup

*Bulletin of the Australian Mathematical Society*

2013-06-01

For an arbitrary set X (finite or infinite), denote by I(X) the symmetric inverse semigroup of partial injective transformations on X. For an element a in I(X), let C(a) be the centralizer of a in I(X). For an arbitrary a in I(X), we characterize the elements b in I(X) that belong to C(a), describe the regular elements of C(a), and establish when C(a) is an inverse semigroup and when it is a completely regular semigroup. In the case when the domain of a is X, we determine the structure of C(a) in terms of Green's relations.

## Social