Janusz Konieczny
Professor, Mathematics University of Mary Washington
- Fredericksburg VA
Janusz Konieczny is a professor of mathematics at the University of Mary Washington.
University of Mary Washington
View more experts managed by University of Mary Washington
Social
Biography
Areas of Expertise
Accomplishments
Alumni Association Outstanding Young Faculty Member Award
1996-01-01
Awarded by the University of Mary Washington Alumni Association.
Mary Washington Faculty Development Grant
2011-01-01
Awarded by the University of Mary Washington.
Education
Jagiellonian University
M.S.
Mathematics
1978
Jagiellonian University
M.S.
Computer Science
1982
Pennsylvania State University
Ph.D.
Mathematics
1992
Event Appearances
The Commuting Graph of the Symmetric Inverse Semigroup
Analysis, Logic and Physics Seminar Richmond, VA
2013-09-27
Articles
Centralizers in the infinite symmetric inverse semigroup
Bulletin of the Australian Mathematical Society2013-06-01
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.
Conjugation in semigroups
Journal of Algebra2014-02-01
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.
Automorphism groups of endomorphism monoids of free G-sets
Asian-European Journal of Mathematics2014-03-01
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).
The largest subsemilattices of the endomorphism monoid of an independence algebra
Linear Algebra and its Applications2014-10-01
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.
The commuting graph of the symmetric inverse semigroup
Israel Journal of Mathematics2015-04-01
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.
