, Volume 23, Issue 2, pp 179–195

Rook Poset Equivalence of Ferrers Boards


DOI: 10.1007/s11083-006-9039-8

Cite this article as:
Develin, M. Order (2006) 23: 179. doi:10.1007/s11083-006-9039-8


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.

Key words

Schubert varietiesFerrers boardsrook equivalencerook placements

Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  1. 1.American Institute of MathematicsPalo AltoUSA