**Jean-Paul DOIGNON**

U.L.B. c.p. 216,

Bd du triomphe,

1050 Bruxelles,

Belgium

doignon@ulb.ac.be

Symposium: *Order Polytopes*
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**Abstract:**

During the 1960's and 1970's, the same geometric object emerged from a model of binary choice in the mathematical theory of preferences, and from an optimization problem in operations research. It was called either the 'binary choice polytope' or the 'linear ordering polytope'. In both communities of research, progress was made in the study of this polytope (after and before the link was noticed). However, several intriguing problems remain open. Surprising connections with other mathematical subjects in combinatorics were discovered, for instance with stability- critical graphs. More recently, many similar polytopes were introduced for other species of order relations, e.g., linear signed orders, semiorders, interval orders, biorders, etc. Also, relations among these polytopes and other similar ones proved useful to gain better understanding of their structures. And these polytope offer a nice opportunity to apply and to test general methods for producing facets or for solving integer linear programming problems.

The goal of the symposium is to bring together researchers from various disciplines to foster cross-interactions and to disseminate the latest contributions in the theory and applications of order polytopes.

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