FLAG-SHAPED BLOCKERS OF 123-AVOIDING PERMUTATION MATRICES

A blocker of 123-avoiding permutation matrices refers to the set of zeros contained within an n × n 123-forcing matrix. Recently, Brualdi and Cao provided a characterization of all minimal blockers, which are blockers with a cardinality of n. Building upon their work, a new type of blocker, flag-shaped blockers, which can be seen as a generalization of the L-shaped blockers defined by Brualdi and Cao, are introduced. It is demonstrated that all flag-shaped blockers are minimum blockers. The possible cardinalities of flag-shaped blockers are also determined, and the dimensions of subpolytopes that are defined by flag-shaped blockers are examined.