# Communicating Mathematics

Share this page *Edited by *
*Timothy Y. Chow; Daniel C. Isaksen*

This volume contains the proceedings of a conference held in July, 2007 at
the University of Minnesota, Duluth, in honor of Joseph A. Gallian's 65th
birthday and the 30th anniversary of the Duluth Research Experience for
Undergraduates.

In keeping with Gallian's extraordinary expository ability and broad
mathematical interests, the articles in this volume span a wide variety of
mathematical topics, including algebraic topology, combinatorics, design
theory, forcing, game theory, geometry, graph theory, group theory,
optimization, and probability.

Some of the papers are purely expository while others are research
articles. The papers are intended to be accessible to a general
mathematics audience, including first-year or second-year graduate
students. This volume should be especially useful for mathematicians
seeking a new research area, as well as those looking to enrich
themselves and their research programs by learning about problems and
techniques used in other areas of mathematics.

#### Readership

Graduate students and research mathematicians interested in algebra, discrete mathematics, geometry, or probability.

# Table of Contents

## Communicating Mathematics

- Contents v7 free
- Preface vii9 free
- A journey of discovery: Orthogonal matrices and wireless communications 111 free
- Probabilistic expectations on unstructured spaces 1121
- A beginner's guide to forcing 2535
- Higher order necessary conditions in smooth constrained optimization 4151
- Hamiltonian paths and hyperbolic patterns 5161
- When graph theory meets knot theory 6777
- Can an asymmetric power structure always be achieved? 8797
- McKay's canonical graph labeling algorithm 99109
- A multiplicative deformation of the Möbius function for the poset of partitions of a multiset 113123
- Communicating, mathematics, communicating mathematics – Joe Gallian style 119129
- Fair allocation methods for coalition games 127137
- Sums-of-squares formulas 157167
- Product-free subsets of groups, then and now 169179
- Generalizations of product-free subsets 179189
- What is a superrigid subgroup? 189199
- Averaging points two at a time 207217
- Vertex algebras as twisted bialgebras: On a theorem of Borcherds 223233