2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142781Chessboard complexes and their relatives have been one of important recurring themes of topological combinatorics. Closely related ``cycle-free chessboard complexes'' have been recently introduced by Ault and Fiedorowicz as a tool for computing symmetric analogues of the cyclic homology of algebras. We study connectivity properties of these complexes and prove a result that confirms a strengthened conjecture of Ault and Fiedorowicz.This is an extended version where the tightness of the bound in the case n=3k+2 is establishedAlgebraic TopologyCombinatoricstext