Mathematics Commons^™

Cyclicizers, Centralizers, And Normalizers, David Patrick, Eric Wepsic

Mathematical Sciences Technical Reports (MSTR)

Our goal is to define the cyclicizer, which is analogous to the centralizer and normalizer, and to examine groups in which these subsets have certain special properties.

Counting Centralizers In Finite Groups, Sarah Marie Belcastro, Gary J. Sherman

Mathematical Sciences Technical Reports (MSTR)

We discuss various results on the number of commuting pairs and the sizes of the centralizers of a group.

Integer Triangles With Rational Medians, Bart Goddard, Dale Mesner

Mathematical Sciences Technical Reports (MSTR)

A characterization of all integer-sided triangles with a rational median is given, similar to the categorization of Pythagorean triangles. An infinite family of integer-sided triangles with two rational medians is given, along with several examples of three rational medians. All examples come from solutions to systems of quadratic Diophantine equations.

An Upper Bound For 3-Rewriteability In Finite Groups, Jordan Ellenberg

Mathematical Sciences Technical Reports (MSTR)

An ordered triple of group elements (x,y,z) is said to be rewriteable if the product xyz is equal to one of the products xzy, yxz, yzx, zxy, zyx. In the present paper, we shall ask the following question: how rewriteable can a finite group be if its derived group has order greater than 2?

Finite Abelian Groups In Which The Probability Of An Automorphism Fixing An Element Is Large, Gary J. Sherman

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group and let A be its automorphism group. We obtain various results on the probability that a random element of A fixes a random element of G.

Dihedral Rewriteability, Cheryl P. Grood

Mathematical Sciences Technical Reports (MSTR)

In this paper we compute the probability that an n-tuple for a group G is S-rewritable for a given set S of permutations for several classes of groups.

Some Facts About Cwat-Sets, Martin Wattenburg

Mathematical Sciences Technical Reports (MSTR)

In [1] and [2], Sherman and Atkins, in connection with a problem in statistics, introduced a generalization of the concept of a subgroup of Z₂. These generalized subgroups, which we call CWAT-sets (where "CWAT" is an acronym for "Closed With A Twist" ), have a rich algebraic structure. In this paper we establish some simple combinatorial facts about CWAT-sets, as well as provide two construction methods, prove a divisibility theorem, and make a classification conjecture.

A Numerical Approach To Rewriteability In Finite Groups, J.L. Leavitt, G.J. Sherman, M.E. Walker

Mathematical Sciences Technical Reports (MSTR)

In this paper we compute the probability that an n-tuple for a group G is S-rewritable for a given set S of permutations for several classes of groups.

Maximal Order Three-Rewriteable Subgroups Of Symmetric Groups, John T. O'Bryan

Mathematical Sciences Technical Reports (MSTR)

Recently, Burns and Goldsmith [2] characterized the maximal order Abelian subgroups of the symmetric groups using elementary techniques and the results of Hoffman [5]. This classification could also be directly inferred from the results of Kovacs and Praeger [7]. A natural extension would be to consider the weaker, more general form of commutativity, three-rewriteability. The purpose of this paper is to completely characterize the maximal order three-rewriteable subgroups of the symmetric groups.

How Hamiltonian Can A Finite Group Be?, G.J. Sherman, T.J. Tucker, M.E. Walker

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.

Fibonacci Sequences In Finite Groups, Steven W. Knox

Mathematical Sciences Technical Reports (MSTR)

This paper extend the notion of Fibonacci sequence mod m to Fibonacci sequences in finite groups.

Sets Of Typical Subsamples, Joel Atkins, G.J Sherman

Mathematical Sciences Technical Reports (MSTR)

A group theoretic condition on a set of subsamples of a random sample from a continuous random variable symmetric about 0 is shown to be sufficient to provide typical values for 0.

Rewriteable Sequencings Of Groups, Jeanne Nielsen

Mathematical Sciences Technical Reports (MSTR)

A finite group is called P_n-sequenceable if its nonidentity elements can be listed x₁ , x₂ , ..., x_k so that the product x _i x _i+i · · · x _i+n-1 can be rewritten in at least one nontrivial way for all i. It is shown that S_n , A_n , D_n are P₃-sequenceable, that every finite simple group is P₄ -sequenceable, and that every finite group is P_s-sequenceable. It is conjectured that every finite group is P₃-sequenceable.

Linear Estimation: The Kalman-Bucy Filter, William Douglas Schindel

Graduate Theses - Mathematics

The problem of linear dynamic estimation, its solution as developed by Kalman and Bucy, and interpretations, properties and illustrations of that solution are discussed. The central problem considered is the estimation of the system state vector X, describing a linear dynamic system governed by

dx/dt = F(t)X(t) + G(t)U(t)

Y(t) = H(t)X(t) + V(t)

for observations of Y (system output), where V is a random observation-corrupting process, and U is a random system driving process.

An extension of the Kalman-Bucy filter to estimation in the absence of priori knowledge of the random process U and V is developed and illustrated.