Markov Chains and Schubert Polynomials

A Markov chain on the symmetric group which is Schubert positive? (Lauren Williams and Thomas Lam), to appear in Experimental Mathematics.

We define a multivariate Markov chain on the symmetric group with remarkable enumerative properties. We conjecture that the components of its stationary distribution can be written as positive combinations of Schubert polynomials.

http://math.berkeley.edu/~williams/papers/qMarkov5.pdf