Database of Permutation Pattern Avoidance

Entry P0011

ID:          P0011
Patterns:    4 2 3 1
             3 5 1 4 2
             4 2 5 1 3
             3 5 1 6 2 4
Title:       The associated Schubert variety is defined by inclusions
             The number of regions in the inversion hyperplane arrangement associated with the permutation is equal to the number of elements below the permutation in the Bruhat order
References:  V. Gasharov and V. Reiner, Cohomology of smooth Schubert varieties in partial flag manifolds, J. Lond. Math. Soc. 66 (2002), 550-562.
             A. Hultman, S. Linusson, J. Shareshian, J. Sjöstrand, From Bruhat intervals to intersection lattices and a conjecture of Postnikov, J. Combin. Theory Ser. A, 116(3) (2009), 564-580.
             M.H. Albert and R. Brignall, Enumerating indices of Schubert varieties defined by inclusions, to appear in J. Combin. Theory Ser. A
Enumeration: (1-3x-2x^2-(1-x-2x^2)\sqrt{1-4x})/(1-3x-(1-x+2x^2)\sqrt{1-4x})
OEIS:        A213090
Contributor: Vic Reiner - November 15, 2005
             Richard Stanley - October 8, 2007
             Joel Lewis - February 3, 2014
             Charles Greathouse - October 20, 2015