[Discrete-math-seminar] Wednesday May 9 DAM seminar: Oscar Ortega (Part 2)

[Robert Ellis]

Please join us for part 2 of the combinatorics research seminar, the last 
regularly scheduled for spring semester:

Wednesday, May 9 11:00pm
Speaker: Oscar Ortega (Applied Mathemathics IIT)
Title: The Mean Function on Finite Trees

Abstract: A MEAN of a sequence S=(x_1,x_2,...,x_n) of elements of a finite 
metric space (X,d) is an element x for which 
d^2(x,x_1)+d^2(x,x_2)+...+d^2(x,x_n)  is minimum. The function MEAN with 
domain the set of all finite sequences on X and defined by

 	Mean(S)={x: x is a mean of S}

is called the mean function on X.

The first characterization of the mean function on trees in the continuous 
case was given by Holzmann in 1990 and a different characterization was 
given by R. Vohra in 1996. In the continuous case means that the metric 
space (X,d) is not finite; the edges of the tree are curves of finite 
length and the Mean(S) contains only one element that could be a vertex or 
an element of an edge. In this talk an axiomatic characterization of the 
mean function on finite trees will be presented.