05C50 Online Seminar: Geir Dahl

In combinatorial matrix theory (CMT) one studies properties of combinatorial matrices, i.e., matrices with entries 0, 1 and -1. For instance, permutation matrices, i.e., (0,1)-matrices with exactly one 1 in every row and column, are interesting. There are basic and challenging questions for permutation matrices and related matrix classes. This is what this talk will be about.

One of the roots of CMT is work done by Frobenius and, slightly later, by Konig. We present some of these ideas and results, including the classical Frobenius-Konig theorem, along with some connections to related mathematical areas. Also, some recent work with Richard Brualdi on an extension of the Frobenius-Konig theorem will be discussed, and there we will see a connection to a very powerful theorem by Hoffman.

A main goal is to present this in a non-technical way, and hopefully the topic may be of interest in the 05C50-community and its neighborhood!