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. He is the author of numerous research articles on the theory of algebraic semigroups. His most recent articles have appeared in the Bulletin of the American Mathematic Society, the Central European Journal of Mathematics, Mathematische Nachrichten, and the European Journal of Combinatorics.
Recently, he has given presentations at the Workshop on Universal Algebra, Complexity and Constraint Satisfaction Problems in Lisbon, Portugal and at the Center of Algebra of the University of Lisbon. Dr. Konieczny was awarded a 2011-2012 Mary Washington Faculty Development Grant for the project “Conjugacy in Semigroups."
Areas of Expertise (6)
Mary Washington Faculty Development Grant (professional)
Awarded by the University of Mary Washington.
Alumni Association Outstanding Young Faculty Member Award (professional)
Awarded by the University of Mary Washington Alumni Association.
Pennsylvania State University: Ph.D., Mathematics 1992
Jagiellonian University: M.S., Computer Science 1982
Jagiellonian University: M.S., Mathematics 1978
Event Appearances (1)
The Commuting Graph of the Symmetric Inverse Semigroup
Analysis, Logic and Physics Seminar Richmond, VA
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.
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.
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).
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.
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.