Birational Rowmotion and Coxeter-Motion on Minuscule Posets

Birational rowmotion is a discrete dynamical system on the set of all positive real-valued functions finite poset, which birational lift combinatorial order ideals. It known that for minuscule poset has equal to Coxeter number, and exhibits file homomesy phenomenon refined ideal cardinality statistics. In this paper we generalize these results setting. Moreover, as generalization promotion product two chains, introduce Coxeter-motion posets, prove it enjoys periodicity homomesy.