Matching theory and Barnette's conjecture

Instrument dependency of Kubelka-Munk theory in computer color matching

Different industries are usually faced with computer color matching as an important problem. The most famous formula which is commonly used for recipe prediction is based on Kubelka-Munk K-M theory. Considering that spectrophotometer’s geometry and its situation influence the measured spectral values, the performance of this method can be affected by the instrument. In the present study, three ...

A Conjecture on random bipartite matching

In this note we put forward a conjecture on the average optimal length for bipartite matching with a finite number of elements where the different lengths are independent one from the others and have an exponential distribution. The problem of random bipartite matching (or assignment) is interesting both from the point of view of optimisation theory and of statistical mechanics [1, 2, 3, 4]. Ea...

Improved bounds for Erdős' Matching Conjecture

Article history: Received 7 June 2012 Available online 24 February 2013

Matching Theory

Representation Theory, Topological Field Theory, and the Andrews-curtis Conjecture

We pose a representation-theoretic question motivated by an attempt to resolve the Andrews-Curtis conjecture. Roughly, is there a triangular Hopf algebra with a collection of self-dual irreducible representations Vi so that the product of any two decomposes as a sum of copies of the Vi, and ∑ (rank Vi) 2 = 0? This data can be used to construct a “topological quantum field theory” on 2complexes ...