Room 326

Markov chains based on Jeu de Taquin

Arvind Ayyer

Department of Mathematics, Indian Institute of Science, Bengaluru

Schutzenberger extended his own operation of Jeu de Taquin on Young
tableaux to linear extensions of arbitrary posets. We use this operation
to define Markov chains on the set of linear extensions, and write down
explicit formulas for their stationary distributions. When the posets are
antichains, one obtains the well-known Tsetlin library. When the posets
are the so-called down forests, we can prove formulas for the eigenvalues,
with their multiplicities, of the generators. This is joint work with
Steve Klee and Anne Schilling.