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                * Princeton Discrete Math Seminar *
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Date: Thursday 27th October, 2.15 in Fine Hall 224
 
Speaker: Stefan van Zwam, Princeton

Title: Beyond Total Unimodularity

A matrix is TOTALLY UNIMODULAR if the determinant of each square submatrix 
is in {-1, 0, 1}. Such matrices are a cornerstone of the theory of integer 
programming. The deepest result on such matrices is Seymour's decomposition 
theorem. The only known way to test efficiently whether a matrix is totally 
unimodular makes use of this theorem. 

Recently, Whittle introduced several classes of matrices with similar 
properties: the determinants of the submatrices are restricted to a certain 
set. In this talk I will discuss some results from the theory of totally 
unimodular matrices from the point of view of matroid theory, and outline 
which of those results will, won't, or might generalize to Whittle's classes. 
In particular I will sketch an extension of Kirchhoff's matrix tree theorem 
to quaternionic unimodular matrices. That result is joint work with 
Rudi Pendavingh.

 
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Next week: Fall recess, no seminar

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