Time: 9h30, Thursday, October 13, 2016
Location: Room 201, A5, Institute of Mathematics, 18, Hoang Quoc Viet, Ha Noi, Viet Nam
Abstract: The first part of the talk will be devoted to the notion of the rank of configurations on a graph. Configurations (also called divisors) are defined by assigning integer values (possibly negative) to the vertices of the graph. The rank of a configuration was defined by Baker and Norine in a seminal paper appeared in 2007. They also introduced an involution on the set of  configurations and proved a formula on  the ranks of two configurations exchanged by this involution.
This formula was called "Riemann Roch formula for graphs".
In the second part of the talk we will focus on complete graph and examine the properties of the involution introduced by Baker and Norine on these graphs. It could be  translated  into an involution on Dyck words which leads to some new combinatorial results on them and to some conjecture. The definition of Dyck words (or paths) will be recalled and also their main properties.