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Lectures and Colloquia during the semester



November 18, 2002

Freie Universität Berlin - Institut für Informatik
Takustraße 9
14195 Berlin
Room 005           - map -
Lecture - 14:15

Graham Brightwell- School of Economics, London

Bounding the Number of Linear Extensions

Abstract: A linear extension of a partially ordered set P is a linear order on the same ground-set that is consistent with the partial order. The number e(P) of linear extensions is a fundamental parameter of the partial order.

In the particular case where P is the Boolean lattice 2^n, Sha and Kleitman proved the appealing -- and non-trivial -- bound

e(2^n) ≤ \prod_{i=0}^n binom{n}{i}^{binom{n}{i}}.

We give two alternative proofs of this bound, showing how the result fits in with a more general theory based around Stanley's Theorem on the volume of the chain polytope of a partial order.


Colloquium - 16:00

Ares Ribó Mor - Freie Universität Berlin

Locked and Unlocked Self-Touching Configurations

Abstract: In the last years, there has been much progress in the study of planar linkages that are locked, in the sense that there exists no motion into some other configuration preserving the bar lengths and without bar crossings. In the plane, the combinatorial planar embedding of a linkage is specified, since it can not change by a motion that avoids crossings.

Self-touching frameworks, in which multiple edges converge to geometrically overlapping configurations, are of great interest in this context, since locked linkages are often based on approximations to them.

In this talk we will describe some open problems with planar linkages in the plane in which I am working on. The tools used in this topic are often geometric planar properties combined with techniques from rigidity theory, as first-order rigidity and equilibrium stresses.


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