A formula for simplicial tree-numbers of matroid complexes. (April 2016)

• Record Type: Journal Article
• Authors: Kook, Woong; Lee, Kang-Ju
• Is Part Of: European journal of combinatorics. Volume 53(2016:Apr.)
• Page Start: 59
• Page End: 65
• Publication Date: 2016-04
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2015.11.001
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We give a formula for the simplicial tree-numbers of the independent set complex of a finite matroid M as a product of eigenvalues of the total combinatorial Laplacians on this complex. Two matroid invariants emerge naturally in describing the multiplicities of these eigenvalues in the formula: one is the unsigned reduced Euler characteristic of the independent set complex and the other is the β -invariant of a matroid. We will demonstrate various applications of this formula including a "matroid theoretic" derivation of Kalai's simplicial tree-numbers of a standard simplex.