login
Triangular array: rows are the f-vectors of simplicial complexes dual to permutohedra of type D_n.
2

%I #5 Sep 16 2020 05:03:07

%S 1,1,1,1,4,4,1,14,36,24,1,48,240,384,192,1,162,1440,4160,4800,1920,1,

%T 536,8216,38400,76800,69120,23040,1,1738,45528,326032,1008000,1532160,

%U 1128960,322560,1,5536,247456,2634240,11854080,27095040,33116160

%N Triangular array: rows are the f-vectors of simplicial complexes dual to permutohedra of type D_n.

%C The root systems of type D_n are only defined for n >= 2. It is convenient to add two initial rows to the array to give a lower triangular array. See A066094 for the corresponding array of h-vectors of type D permutohedra.

%F E.g.f. : ((1 + x)*z - exp(z))/(x*exp(2*z) - (1 + x)) = 1 + x*z + (1 + 4*x + 4*x^2)*z^2/2! + (1 + 14*x + 36*x^2 + 24*x^3)*z^3/3! + ... .

%F Row sums A080254.

%e The triangle begins

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

%e =====================================

%e 0..|..1

%e 1..|..1.....1

%e 2..|..1.....4.....4

%e 3..|..1....14....36....24

%e 4..|..1....48...240...384...192

%e 5..|..1...162..1440..4160..4800..1920

%e ...

%Y Cf. A019538 (f-vectors type A permutohedra), A080254 (row sums), A066094 (h-vectors type D permutohedra), A145901 (f-vectors type B permutohedra).

%K easy,nonn,tabl

%O 0,5

%A _Peter Bala_, Oct 29 2008

%E Corrected typo. - _Peter Bala_, Oct 31 2008