A simple definition for the universal Grassmannian order

Authors:
Curtis D. Bennett;Lakshmi Evani;David Grabiner
Affiliations:
Department of Mathematics, Loyola Marymount University, Los Angeles, CA;Department of Mathematics, Bowling Green State University, Bowling Green, OH;7318 Eden Brook Dr. #123, Columbia, MD
Venue:
Journal of Combinatorial Theory Series A
Year:
2003

Citing 3
Cited 1

Enumerative combinatorics

Enumerative combinatorics
A moniod for the Grassmannian Bruhat order

European Journal of Combinatorics
Partial orders generalizing the weak order on Coxeter groups

Journal of Combinatorial Theory Series A

Partial orders generalizing the weak order on Coxeter groups

Journal of Combinatorial Theory Series A

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Abstract

In this paper, we provide a combinatorial definition of the Universal Grassmannian order (or the Grassmannian Bruhat order) of Bergeron and Sottile. This defines the order in terms of inversions, and thus the order can be viewed as a generalization of the weak order for Coxeter groups. Finally, we use this understanding of the order to analyze the generating function of the number of elements at rank n in this order.