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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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0
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1, 2, 6, 20, 71, 260, 971, 3670, 13968, 53369, 204352, 783408, 3005284, 11533014, 44267854, 169935041, 652385639, 2504613713, 9615798516, 36917689075, 141737959416, 544175811783, 2089262741393, 8021347093432, 30796530585417, 118237818141689, 453953210838465
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OFFSET
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1,2
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COMMENTS
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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, Ann. Comb. 11 (2007), no. 2, 195-212.
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LINKS
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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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MATHEMATICA
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LinearRecurrence[{6, -9, 3, 1, -8, -1, 1}, {1, 2, 6, 20, 71, 260, 971}, 27] (* Jean-François Alcover, Feb 02 2019 *)
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PROG
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(PARI) lista(nt) = { my(x = 'x + 'x*O('x^nt) ); P = (-x^7-2*x^6+2*x^5+x^4-3*x^3+4*x^2-x) / (x^7-x^6-8*x^5+x^4+3*x^3-9*x^2+6*x-1); print(Vec(P)); } \\ Michel Marcus, Mar 17 2013
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CROSSREFS
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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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EXTENSIONS
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STATUS
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approved
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