Comment on Volume 17(1), article N27 (published May 20, 2010)

Bijection Between Bigrassmannian Permutations Maximal below a Permutation and its Essential Set Masato Kobayashi

Comment by the author, May 23, 2010:

In September 2009 Reiner, Woo and Yong discussed a correspondence between Fulton's essential set of a given permutation and minimal (in Bruhat order) elements of the set of permutations which are not strictly below it. It is interesting that every element in the latter set is necessarily bigrassmannian. See:

V. Reiner, A. Woo and A. Yong, Presenting the cohomology of a Schubert variety, Sections 1, 2, 4, arXiv:math.CO/08092981v2, 24pp., 2009, to appear in Trans. Amer. Math. Soc.