May 18 – 22, 2026
Virginia Tech
America/New_York timezone

A new combinatorial rank concept and its challenges

May 21, 2026, 2:00 PM
25m
Goodwin Hall 135 (Virginia Tech)

Goodwin Hall 135

Virginia Tech

Minisymposium Talk Combinatorial Matrix Theory Combinatorial Matrix Theory

Speaker

Geir Dahl

Description

We introduce a new rank concept for $(0,\pm 1)$-matrices, called the $\pm$-rank of a $(0,\pm 1)$-matrix. This ``generalizes'' the binary rank and the term rank of (0,1)-matrices. We establish several inequalities relating the different ranks, including ordinary real rank. Moreover, the $\pm$-rank is discussed for certain classes of $(0,\pm 1)$-matrices, such as alternating sign matrices (ASMs), network matrices etc. We also focus on some challenging problems concerning this rank concept, both of theoretical and computationally nature.

Authors

Geir Dahl Prof. Richard Brualdi (University of Wisconsin)

Presentation materials

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