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A129778
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Number of Deodhar elements in the finite Weyl group D_n.
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0
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OFFSET
| 1,1
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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.
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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.
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LINKS
| S. C. Billey and B. C. Jones, Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory.
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EXAMPLE
| 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.
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CROSSREFS
| Cf. A058094.
Sequence in context: A119841 A149905 A149906 * A060797 A124381 A131236
Adjacent sequences: A129775 A129776 A129777 * A129779 A129780 A129781
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KEYWORD
| nonn
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AUTHOR
| Brant Jones (brant(AT)math.washington.edu), May 17 2007
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