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

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%I A129778 #3 Feb 27 2009 03:00:00
%S A129778 2,5,14,48,167,575,1976,6791
%N A129778 Number of Deodhar elements in the finite Weyl group D_n.
%C A129778 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.
%D A129778 S. Billey and G. S. Warrington, Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations, J. Algebraic Combin., 13(2):111-136, 2001.
%D A129778 V. Deodhar, A combinatorial setting for questions in Kazhdan-Lusztig theory, Geom. Dedicata, 36(1): 95-119, 1990.
%H A129778 S. C. Billey and B. C. Jones, <a href="http://www.arXiv.org/abs/math.CO/0612043">Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory</a>.
%e A129778 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.
%Y A129778 Cf. A058094.
%K A129778 nonn
%O A129778 1,1
%A A129778 Brant Jones (brant(AT)math.washington.edu), May 17 2007