Combinatorics of the Rothe diagram
by Richard Brak
Abstract: The Rothe diagram is one of the earliest combinatorial models and appeared in a memoir by Rothe in 1800 concerning simultaneous linear equations. I will discuss a range of combinatorial results that can
be obtained from the diagram. These range from the elementary to
the not so elementary, inversion codes, Coxter words for S n, multiset bijections and a (newish) RSK tableaux correspondence method, the coplactic monoid and, time permitting, crystals bases.
I will also discuss a new bijection, using half of the Rothe diagram, between partially directed walks in a wedge and involutions with no fixed points, conjectured by Rechnitzer, Prellberg and van Rensberg at FPSAC 07.
For More Information: Contact Iwan Jensen I.Jensen@ms.unimelb.edu.au