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Search: id:A109253
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| A109253 |
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Number of elements of the Weyl group of type B where a reduced word contains all of the simple reflections. |
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4
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| 1, 1, 5, 35, 309, 3287, 41005, 588487, 9571125, 174230863, 3513016445, 77760961991, 1875249535941, 48946667107295, 1374949148971597, 41361812577803383, 1326708910645563669, 45201102932347559503
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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This is the analogue of a connected permutation (permutation with no global ascent) in type B.
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LINKS
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N. Bergeron, C. Hohlweg, M. Zabrocki, Posets related to the connectivity set of Coxeter groups
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FORMULA
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o.g.f. g(2x)/g(x) where g(x) = sum_{n>=0} n! x^n
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EXAMPLE
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For n=2, the Weyl group B_2 has 8 elements and is generated by {t,s} with s^2=t^2=(st)^4=1, the elements which have reduced words containing both s and t are st, ts, sts, tst and stst. The other three elements are 1, s, t. Therefore f(2)=5.
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MAPLE
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f:=k->coeff(series(add(2^n*n!*x^n, n=0..k)/add(n!*x^n, n=0..k), x, k+1), x, k);
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CROSSREFS
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Cf. A003319.
Cf. A109281.
Sequence in context: A051406 A000356 A027392 this_sequence A052797 A151344 A015683
Adjacent sequences: A109250 A109251 A109252 this_sequence A109254 A109255 A109256
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KEYWORD
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nonn
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AUTHOR
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Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Aug 19 2005
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