Séminaire Lotharingien de Combinatoire, 82B.50 (2019), 12 pp.

Emily Barnard and Thomas McConville

Lattices from graph associahedra

Abstract. Given a graph G on n vertices, Postnikov defined a graph associahedron P_G as an example of a generalized permutohedron, a polytope whose normal fan coarsens the braid arrangement. Motivated by two general constructions of subalgebras of the Malvenuto-Reutenauer algebra, we consider the poset L_G obtained by orienting the one-skeleton of P_G. Because the normal fan of P_G coarsens the normal fan of the standard permutohedron we obtain a surjection Ψ_G: S_n -> L_G. We characterize the graphs G for which Ψ_G is a lattice quotient map.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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