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The conference, made possible by funding provided by DIMACS, the National Science Foundation, and the Ministere des Affaires Etrangeres of France, attracted an audience of approximately 180 attendees, consisting of graduate students, junior researchers and senior researchers from Austria, Canada, Croatia, France, Germany, India, Isreal, Italy, Japan, Mexico, The Netherlands, Russia, Sweden, and the United States. Originally planned as a small workshop to highlight the vitality of current research in algebraic combinatorics, it was later merged into the FPSAC/SFCA series of annual conferences, becoming the 1994 meeting of this series. It focused on algebraic combinatorics and its connections with enumeration topology, geometry, and theoretical computer science.
The conference program included nine invited hour lectures as well as fory-two contributed presentation. The invited lectures were given by Louis Billera, Anders Bjorner, Ruth Charney, Maylis Delest, Philip Hanlon, David Jackson, Sergei Kerov, Christophe Reutenauer, and Sheila Sundaram. (One of the original invited speakers was forced to cancel just prior to the conference, and his spot was filled by one of the organizers.)
All of these lectures appear in this volume. Articles related to the contributed presentations appear separately in a special issue of the journal Discrete Mathematics, edited by Rodica Simion.
Loosely speaking, algebraic combinatorics involves the use of the techniques from algebra, algebraic topology, and algebraic geometry in the solution of combinatorial problems, or the use of combinatorial methods to attack problems in these areas. The combinatorial problems amenable to algebraic methods can arise in these or other areas of mathematics, or from areas such as computer science, operations research, physics, chemistry and, more recently, biology, Because of this interplay with many fields of mathematics and science, algebraic combinatorics is an area in which a wide variety of ideas and methods come together. We hope the papers that follow give some indication of this rich interaction.
Preface ix The Combinatorics of Permutation Polytopes Louis J. Billera and A. Sarangarajan 1 Nonpure Shellability, f-Vectors, Subspace Arrangements and Complexity Anders Bjorner 25 Metric Geometry: Connections with Combinatorics Ruth Charney 55 Algebraic Languages: A Bridge between Combinatorics and Computer Science Maylis Delest 71 A Survey of Combinatorial Problems in Lie Algebra Homolgy Phil Hanlon 89 Algebraic and Analytic Approaches for the Genus Series for 2-Cell Embeddings on Orientable and Nonorientable Surfaces D.M. Jackson 115 The Boundary of Young Lattice and Random Young Tableaux S. Kerov 133 A Survey of Noncommutative Rational Series Christophe Reutenauer 159 Plethysm, Partitions with an Even Number of Blocks and Euler Numbers Shelia Sundaram 171