

A129778


Number of Deodhar elements in the finite Weyl group D_n.


0




OFFSET

1,1


COMMENTS

The Deodhar elements are a subset of the fully commutative elements. If w is Deodhar, there are simple explicit formulas for all the KazhdanLusztig polynomials P_{x,w} and the KazhdanLusztig basis element C'_w is the product of C'_{s_i}'s corresponding to any reduced expression for w.


REFERENCES

S. Billey and G. S. Warrington, KazhdanLusztig polynomials for 321hexagonavoiding permutations, J. Algebraic Combin., 13(2):111136, 2001.
V. Deodhar, A combinatorial setting for questions in KazhdanLusztig theory, Geom. Dedicata, 36(1): 95119, 1990.


LINKS

Table of n, a(n) for n=1..8.
S. C. Billey and B. C. Jones, Embedded factor patterns for Deodhar elements in KazhdanLusztig theory.


EXAMPLE

a(4)=48 because there are 48 fully commutative elements in D_4 and since the first nonDeodhar fullycommutative element does not appear until D_6, these are all of the Deodhar elements in D_4.


CROSSREFS

Cf. A058094.
Sequence in context: A119841 A149905 A149906 * A060797 A124381 A131236
Adjacent sequences: A129775 A129776 A129777 * A129779 A129780 A129781


KEYWORD

nonn


AUTHOR

Brant Jones (brant(AT)math.washington.edu), May 17 2007


STATUS

approved



