A129778 Number of Deodhar elements in the finite Weyl group D_n.

2, 5, 14, 48, 167, 575, 1976, 6791

Offset: 1

Author

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

Keywords

• nonn

Comments

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

Examples

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

References

• S. Billey and G. S. Warrington, Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations, J. Algebraic Combin., 13(2):111-136, 2001.
• V. Deodhar, A combinatorial setting for questions in Kazhdan-Lusztig theory, Geom. Dedicata, 36(1): 95-119, 1990.

Links

• S. C. Billey and B. C. Jones, Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory.

Crossrefs

Cf. A058094.