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Mathematics & Statistics

# Discrete Mathematics (Leader: Prof. Greg McColm)

## Monday, November 18, 2002

Title
Speaker
Time
Place

Counting Blocks in Dimension 2, Part II
Nataša Jonoska
4:00pm-5:00pm
PHY 118

## Monday, November 4, 2002

Title
Speaker
Time
Place

Counting Blocks in Dimension 2
Nataša Jonoska
4:00pm-5:00pm
PHY 118

Abstract

We consider subsets of the set of all actions of $$Z\times Z$$ onto a finite alphabet. These subsets (called shifts) are closed under the multiplication with the generators $$(0,1)$$ and $$(1,0)$$ and topologically closed (alphabet has discrete topology and the actions are equipped with the product topology).

We introduce the notion of “uniform transitivity” which is stronger than topologicaltransitivity, but, it implies topological entropy-minimal systems.

## Monday, October 28, 2002

Title
Speaker
Time
Place

Forbidding and Enforcing Systems, Part II
Daniela Genova
4:00pm-5:00pm
PHY 118

## Monday, October 21, 2002

Title
Speaker
Time
Place

Forbidding and Enforcing Systems
Daniela Genova
4:00pm-5:00pm
PHY 118

Abstract

We present a new way of defining classes of formal languages through a set of forbidden subwords and a set of enforced words. Forbidding and enforcing systems were inspired by chemical properties of DNA and actions of restriction enzymes. These systems will be presented through description of several graph theoretical problems and some topological observations will be discussed.

## Monday, October 14, 2002

Title
Speaker
Time
Place

Algebraic Characterizations of Graph Regularity Conditions
Brian Curtin
4:00pm-5:00pm
PHY 118

Abstract

A theorem of algebraic graph theory can be stated as follows: A finite simple connected graph is regular if and only if the all-ones matrix spans an ideal of the adjacency algebra. We show that several other graph regularity conditions have ideal theoretic characterizations in appropriate algebras.

## Monday, October 7, 2002

Title
Speaker
Time
Place

Complexity Measures and Least Fixed Point Logic
Greg McColm
4:00pm-5:00pm
PHY 118

Abstract

We will look at a time complexity measure and a space complexity measure on Least Fixed Point logic. We will use the algebraic approach of Moschovakis (~1980) and Hodges that the audience seems to prefer.

## Monday, September 30, 2002

Title
Speaker
Time
Place

The Foundations of Least Fixed Point Logic
Greg McColm
4:00pm-5:00pm
PHY 118

Abstract

This will be a basic introduction of least fixed point logic, from Tarski to Moschovakis. We will conclude with a look at two complexity measures.

## Monday, September 23, 2002

Title
Speaker
Time
Place

The Number of Recursion Variables
Greg McColm
1:00pm-2:00pm
PHY 109

Abstract

The Number of Recursion Variables (also called “dimension” or “arity” is a space-complexity measure introduced two decades ago. We review its prehistory and its history, mostly in the logic of First Order Logic $$+$$ Least Fixed Points, and then look at a conjecture I'm launching.

## Monday, September 16, 2002

Title
Speaker
Time
Place

Combinatorial and Inverse Relations, Part II
1:00pm-2:00pm
PHY 109

## Thursday, September 12, 2002

Title
Speaker
Time
Place

Combinatorial and Inverse Relations
We show how generalized Taylor series lead to combinatorial identities and inverse relations. One example is a two parameter family of matrices $$A(a,b)$$ with the property $$A(a,b)A(b,c)=A(a,c)$$. Also $$A^{-1}(a,b)=A(b,a)$$. No differential equations will be used.