0,5

For n>1 and 0 <= k <= n, a(n,k) is the number of compatible k-sets of cluster variables in Fomin and Zelevinsky's 'cluster algebra' of finite type D_n.

Triangle of f-vectors of the simplicial complexes dual to the generalized associahedra of type D_n (n >= 2). See A145903 for the corresponding triangle of h-vectors. For the triangles of f-vectors of type A and type B associahedra see A033282 and A063007 respectively. [From Peter Bala (pbala(AT)toucansurf.com), Oct 28 2008]

S. Fomin and A. Zelevinsky, Cluster algebras I: Foundations, J. Amer. Math. Soc. 15 (2002) no. 2, 497-529.

S. Fomin and A. Zelevinsky, Y-Systems and generalized associahedra, Ann. of Math. (2) 158 (2003), no. 3, 977-1018.

S. Fomin and A. Zelevinsky, Cluster algebras I: Foundations, J. Amer. Math. Soc. 15 (2002), no. 2, 497-529.

S. Fomin and A. Zelevinsky, Y-systems and generalized associahedra, Ann. of Math. (2) 158 (2003), no. 3, 977-1018.

S. Fomin, N. Reading, Root systems and generalized associahedra, Lecture notes for IAS/Park-City 2004. [From Peter Bala (pbala(AT)toucansurf.com), Oct 28 2008]

Contribution from Peter Bala (pbala(AT)toucansurf.com), Oct 28 2008: (Start)

Triangle begins

n\k|..0....1....2....3....4....5

================================

0..|..1

1..|..1....1

2..|..1....4....4

3..|..1....9...21...14

4..|..1...16...66..100...50

5..|..1...25..160..410..455..182

...

(End)

Cf. A033282, A063007.

A051924 (main diagonal), A145903( h-vectors type D associahedra). [From Peter Bala (pbala(AT)toucansurf.com), Oct 28 2008]

Sequence in context: A128213 A016706 A138679 this_sequence A123588 A106026 A096078

Adjacent sequences: A080718 A080719 A080720 this_sequence A080722 A080723 A080724

easy,nonn,tabl

Paul Boddington (psb(AT)maths.warwick.ac.uk), Mar 07 2003