Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants

We consider planar maps with three boundaries, colloquially called pairs of pants. In the case bipartite controlled face degrees, a simple expression for their generating function was found by Eynard and proved bijectively Collet Fusy. this paper, we obtain an even simpler formula tight pants, namely whose boundaries have minimal length in homotopy class. follow bijective approach based on slice decomposition, which extend introducing new fundamental building blocks bigeodesic triangles diangles, working universal cover triply punctured sphere. also discuss statistics lengths separating loops (non necessarily tight) pants annuli, asymptotics large volume limit.