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NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT
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Geometry-Algebra-Singularities-Combinatorics Seminar
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Posets of multiset partitions and lexicographic shellability
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MIT
Northeastern University 509 Lake Hall 1:30 p.m., Tuesday, June 1, 1999
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Abstract: We generalize the lattice of partitions of {1, ... , n} partially ordered by refinement by removing the assumption that the objects to be partitioned all need to be distinguishable. Ziegler showed that in the special case of the poset of partitions of n identical objects, the order complex is not Cohen-Macaulay for n> 18; this implies that such multiset partition posets are not shellable. We define a cell complex closely related to the order complex and prove that this is shellable for the poset of partitions of any multiset. This implies that these cell complexes have the homotopy type of a wedge of spheres concentrated in top dimension; in some special cases we index these spheres so as to determine the Euler characteristic. We will discuss our proof of shellability, consequent Euler characteristic formulas and two generalized notions of lexicographic shellability which we employ. This is joint work with Robert Kleinberg.
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Geometry-Algebra-Singularities-Combinatorics home page:
http://www.math.neu.edu/~suciu/GASC.html
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