Start Date
31-10-2023 12:00 PM
End Date
31-10-2023 2:00 PM
Description
A blocker of 123-avoiding permutation matrices refers to the set of zeros contained within an π Γ π 123-forcing matrix. Recently, Brualdi and Cao provided a characterization of all minimal blockers, which are blockers with a cardinality of π. Building upon their work, a new type of blocker, flag-shaped blockers, which can be seen as a generalization of the πΏ-shaped blockers defined by Brualdi and Cao, are introduced. It is demonstrated that all flag-shaped blockers are minimum blockers, and the shifting of positions from these blockers is discussed. Lastly, the dimensions of subpolytopes that are defined by flag-shaped blockers are examined.
Included in
Minimum Blockers of 123-Avoiding Permutation Matrices
A blocker of 123-avoiding permutation matrices refers to the set of zeros contained within an π Γ π 123-forcing matrix. Recently, Brualdi and Cao provided a characterization of all minimal blockers, which are blockers with a cardinality of π. Building upon their work, a new type of blocker, flag-shaped blockers, which can be seen as a generalization of the πΏ-shaped blockers defined by Brualdi and Cao, are introduced. It is demonstrated that all flag-shaped blockers are minimum blockers, and the shifting of positions from these blockers is discussed. Lastly, the dimensions of subpolytopes that are defined by flag-shaped blockers are examined.