Markov degree of configurations defined by fibers of a configuration

TL;DR

This paper investigates the Markov degree of configurations derived from fibers of a base configuration, establishing an upper bound related to the base's Markov complexity and applying this to graph incidence matrices and transportation polytopes.

Contribution

It introduces a bound on the Markov degree for fiber-based configurations and applies it to graph incidence matrices and transportation polytopes, including a proof for the Markov degree of two-way transportation polytopes.

Findings

Markov degree is bounded by the Markov complexity of the base configuration.

Markov degree for two-way transportation polytopes is three.

Analysis of configurations from graph incidence matrices.

Abstract

We consider a series of configurations defined by fibers of a given base configuration. We prove that Markov degree of the configurations is bounded from above by the Markov complexity of the base configuration. As important examples of base configurations we consider incidence matrices of graphs and study the maximum Markov degree of configurations defined by fibers of the incidence matrices. In particular we give a proof that the Markov degree for two-way transportation polytopes is three.