2005/02/05 by Mike Develin, Develin, Mike
Mathematics · #06A06 #14M15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.AG #math.CO #msc:06A06 #msc:14M15
paper · pdf · doi:10.48550/arxiv.math/0502107
14 pages, 7 figures
arxiv created 2005/02/05 · openalex publication_date 2005/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A natural construction due to K. Ding yields Schubert varieties from Ferrers boards. The poset structure of the Schubert cells in these varieties is equal to the poset of maximal rook placements on the Ferrers board under the Bruhat order. We determine when two Ferrers boards have isomorphic rook posets. Equivalently, we give an exact categorization of when two Ding Schubert varieties have identical Schubert cell structures. This also produces a complete classification of isomorphism types of lower intervals of 312-avoiding permutations in the Bruhat order.