1,1

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.

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.

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

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.

Cf. A058094.

Sequence in context: A109156 A129867 A119841 this_sequence A060797 A124381 A131236

Adjacent sequences: A129775 A129776 A129777 this_sequence A129779 A129780 A129781

nonn

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