Year: 2026
Type: preprint
Abstract: A stable matching in a bipartite preference system is a matching that has no unmatched pair whose endpoints both prefer each other to their current assignments. Rothblum gave a linear description of the stable marriage polytope, the convex hull of the incidence vectors of stable matchings. We prove that this polytope is box-totally dual integral. The proof uses the affine representation of the stable marriage polytope as an order polytope together with the matricial characterization of box-TDI polyhedra. Since Kiraly and Pap proved that Rothblum's description is totally dual integral, our result further implies that Rothblum's system is box-totally dual integral.
Source: arXiv (Cornell University)
Authors: Barbato, Michele, Lancini, Emiliano
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7221560541