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Search: id:A145903
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| A145903 |
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Generalised Narayana numbers for root systems of type D_n. Triangle of h-vectors of type D associahedra. |
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+0
4
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| 1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 24, 12, 1, 1, 20, 70, 70, 20, 1, 1, 30, 165, 280, 165, 30, 1, 1, 42, 336, 875, 875, 336, 42, 1, 1, 56, 616, 2296, 3500, 2296, 616, 56, 1, 1, 72, 1044, 5292, 11466, 11466, 5292, 1044, 72, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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The generalised Narayana numbers of type D_n (row n of this triangle) are defined as the entries of the h-vector of the simplicial complex dual to the generalised associahedron of type D_n [Fomin & Reading, p.60]. For the corresponding triangle of f-vectors see A080721. For Narayana numbers of root systems of type A and type B see A001263 and A008459 respectively.
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LINKS
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S. Fomin, N. Reading, Root systems and generalized associahedra, Lecture notes for IAS/Park-City 2004.
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FORMULA
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For n >= 2, T(n,k) = binomial(n,k)^2 - n/(n-1)*binomial(n-1,k-1)*binomial(n-1,k).
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EXAMPLE
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Root systems of type D_n are defined only for n >= 2. It seems
convenient to complete the array to form a lower unit triangular matrix.
Triangle starts
n\k|..0....1....2....3....4....5....6
=====================================
0..|..1
1..|..1....1
2..|..1....2....1
3..|..1....6....6....1
4..|..1...12...24...12....1
5..|..1...20...70...70...20....1
6..|..1...30..165..280..165...30....1
...
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CROSSREFS
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A001263, A008459, A051924 (row sums), A080721.
Sequence in context: A157635 A075798 A155864 this_sequence A155795 A009963 A008300
Adjacent sequences: A145900 A145901 A145902 this_sequence A145904 A145905 A145906
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Peter Bala (pbala(AT)toucansurf.com), Oct 28 2008
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