Discrete Morse functions from lexicographic orders

Patricia Hersh

University of Washington

March 16,
refreshments at 3:45pm


A few years ago, Robin Forman established the notion of a discrete Morse function. We will describe a way of constructing a discrete Morse function with a relatively small number of critical cells from any lexicographic order on the saturated chains of a graded poset. This gives a tool for computing poset Möbius functions via the Morse inequalities and for proving that certain poset order complexes are collapsible or homotopy equivalent to a wedge of spheres. In particular, we apply this to the poset of partitions of a multiset. This is joint work with Eric Babson.

Speaker's Contact Info: hersh(at-sign)math.washington.edu

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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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