A Minimal-rank Counterexample to Shellability in the Quasisymmetric Bruhat Order
Year: 2026
Type: article
Abstract: We give a counterexample to Bansal’s shellability conjecture for the quasisymmetric Bruhat order on indexed binary forests. For the forests with codes E = (0, 1, 0, 1, 1, 0, 1) and F = (1, 2, 4), the order complex of (E, F) is the disjoint union of two six-cycles. This complex is a face link in the order complex of (∅, F), so the principal lower interval [∅, F] is not shellable. We verify the cover table by exact forest-polynomial coefficient extraction and show, using recursive coatom orderings in rank six, that seven is the smallest possible rank of a counterexample top. A standalone verifier and the finite coefficient certificate accompany the paper.
Author: Li, Runheng
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225562682