Real toric manifolds associated with chordal nestohedra

Abstract

This paper investigates the rational Betti numbers of real toric manifolds associated with chordal nestohedra. We consider the poset topology of a specific poset induced from a chordal building set, and show its EL-shellability. Based on this, we present an explicit description using alternating $\mathcal{B}$-permutations for a chordal building set $\mathcal{B}$, transforming the computing Betti numbers into a counting problem. This approach allows us to compute the $a$-number of a finite simple graph through permutation counting when the graph is chordal. In addition, we provide detailed computations for specific cases such as real Hochschild varieties corresponding to Hochschild polytopes.

arXiv comment26 pages,6 figures, 3 tables

References in corpus (10)

• Real Root Conjecture fails for five and higher dimensional spheres
• Toric varieties of Loday's associahedra and noncommutative cohomological field theories
• Moment-angle manifolds, 2-truncated cubes and Massey operations
• The Rook Monoid is Lexicographically Shellable
• The Euler and Springer numbers as moment sequences
• Which nestohedra are removahedra?
• EL-Shellability and Noncrossing Partitions Associated with Well-Generated Complex Reflection Groups
• Hochschild lattices and shuffle lattices
• Hochschild polytopes
• The Betti numbers of real toric varieties associated to Weyl chambers of types E7 and E8