Annals of Combinatorics 4 (2000) iii-iv


    Applications of combinatorics to real problems in physics, chemistry, biology, informational science, economics, investment strategies, etc. have seen a rapid expansion in recent years. This may be attributed to several factors: the efforts and successes of combinatorialists to give their subject a firm foundational basis; the recognition by physical scientists that the methods of differential-integral equations and more  traditional mathematics to which they were accustomed did not always meet the needs of a large category of problems in which configurational and organizational aspects dominated; and the awareness of both parties of the mutual benefits to be gained from exchanges of ideas.

    The Los Alamos National Laboratory, because of the interdisciplinary and diverse nature of its scientific activities and the need to produce solutions of applied problems, provided an ideal setting for such an exchange of ideas among the several disciplines. With this in mind, Professor W.Y.C. Chen of Nankai University and Los Alamos, Professor Peter Shiue of The University of Nevada, Las Vegas, Professor Gian-Carlo Rota of Massachusetts Institute of Technology and Director's Fellow at Los Alamos, and I agreed to organize the Conference on Combinatorics and Physics, August 10-12, 1998 at the Laboratory.

    The papers range across a broad spectrum of subject matter in which combinatorics is illustrated to play a significant role:
biological counting problems, directed animals arising in site percolation models, differential equation analogues to symmetric
functions, quantum cohomology, MacMahon's partition analysis, the counting of orbits in chaotic systems, properties of basic
hypergeometric series, the folding of molecular sequences, group representation theory, hidden Yangian symmetries in affine
Lie algebras and their relation to spin chains, spin-models related to knots and links originating from statistical mechanics,
and the relation of the action of braid groups on powers of a vector space to quantum groups. Combinatorial entities seem to be woven into the very fabric of Nature's behavior, at least in our attempts to comprehend it.

    Regrettably, Gian-Carlo Rota's paper "Ten Problems in Combinatorics" does not appear because of his untimely death six months after the conference. By their efforts in the preparation of this volume of Annals of Combinatorics, the authors pay special tribute not only to the contributions that Gian-Carlo Rota made to the foundations of combinatorics, but also to his commitment and effective style of communicating this mathematics to others, especially, physical scientists.

    The organizers are thankful for the support of the conference by the Center for Nonlinear Studies at Los Alamos through the efforts of Shiyi Chen and J.H. Hyman, by the University of Nevada (Las Vegas) through the efforts of Peter Shiue, and by the Laboratory through the use of its organizational and physical facilities. We are also indebted to Birkhuser for dedicating this special volume of Annals of Combinatorics to the conference proceedings.

James D. Louck
Theoretical Division, Mail Stop B210
Los Alamos National Laboratory
Los Alamos, New Mexico 87545

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