Two enriched poset polytopes

Stanley introduced and studied two lattice polytopes, the order polytope and chain polytope, associated to a finite poset. Recently Ohsugi and Tsuchiya introduce an enriched version of them, called the enriched order polytope and enriched chain polytope. In this paper, we give a piecewise-linear bijection between these enriched poset polytopes, which is an enriched analogue of Stanley's transfer map and bijectively proves that they have the same Ehrhart polynomials. Also we construct explicitly unimodular triangulations of two enriched poset polytopes.