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Search: id:A129777
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| A129777 |
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Number of freely-braided hexagon-avoiding permutations in S_n; the freely-braided hexagon-avoiding permutations are those that avoid 3421, 4231, 4312, 4321, 46718235, 46781235, 56718234 and 56781234. |
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1
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| 1, 2, 6, 20, 71, 260, 971, 3670, 13968, 53369, 204352, 783408, 3005284, 11533014, 44267854, 169935041
(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 freely-braided 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.: (-x^7-2x^6+2x^5+x^4-3x^3+4x^2-x) / (x^7-x^6-8x^5+x^4+3x^3-9x^2+6x-1).
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EXAMPLE
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a(8)=3670 because there are 3670 permutations of size 8 that avoid 3421, 4231, 4312, 4321, 46718235, 46781235, 56718234 and 56781234.
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CROSSREFS
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Cf. A058094, A108600.
Sequence in context: A047126 A145138 A000707 this_sequence A108600 A128729 A006027
Adjacent sequences: A129774 A129775 A129776 this_sequence A129778 A129779 A129780
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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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