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Search: id:A129776
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| A129776 |
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Number of maximally-clustered hexagon-avoiding permutations in S_n; the maximally-clustered hexagon-avoiding permutations are those that avoid 3421, 4312, 4321, 46718235, 46781235, 56718234, 56781234. |
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1
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| 1, 2, 6, 21, 78, 298, 1157, 4535, 17872, 70644, 279704, 1108462, 4395045, 17431206, 69144643, 274300461
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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If w is maximally-clustered and hexagon-avoiding, there are simple explicit formulas for all the Kazhdan-Lusztig polynomials P_{x,w}.
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REFERENCES
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Jozsef Losonczy, Maximally clustered elements and Schubert varieties, Preprint (2006), to appear in Annals of Combinatorics.
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LINKS
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H. Denoncourt and B. Jones, The enumeration of maximally clustered permutations.
B. Jones, Kazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations.
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FORMULA
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G.f.: (3x^6+x^5-5x^4+7x^3-5x^2+x) / (-3x^6+4x^5+8x^4-14x^3+15x^2-7x+1).
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EXAMPLE
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a(8)=4535 because there are are 4535 permutations of size 8 that avoid 3421, 4312, 4321, 46718235, 46781235, 56718234 and 56781234.
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CROSSREFS
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Cf. A058094, A108600.
Adjacent sequences: A129773 A129774 A129775 this_sequence A129777 A129778 A129779
Sequence in context: A101907 A063023 A124292 this_sequence A129775 A054515 A052300
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KEYWORD
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nonn
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AUTHOR
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Brant Jones (brant(AT)math.washington.edu), May 17 2007
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