The combinatorial Laplacian of the Tutte complex (Q5945616)

For a family of boundary maps on the Tutte complex defined for an ordered matroid, a combinatorial description of a basis of eigenvectors for the combinatorial Laplacian is given, extending work of \textit{W. Kook, V. Reiner} and \textit{D. Stanton} [J. Am. Math. Soc. 13, No. 1, 129-148 (2000; Zbl 0940.05021)]. As an application a duality theorem for the cohomology of Orlik-Solomon algebras is proven.