

A153255


Arises in enumerating orientable small covers over cubes.


0



1, 1, 1, 4, 43, 1156, 74581, 11226874, 3862830343, 2990426173816, 5144550664291081, 19470823356314891254, 160782837107861606438923, 2876650791540557329654540276, 110853465572134076561454447710221
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OFFSET

1,4


COMMENTS

A small cover, as defined by Davis and Januszkiewicz, is an ndimensional closed smooth manifold M with a smooth action of standard real torus (Z_2)^2 action such that the action is locally isomorphic to a standard action of (Z_2)^2 on R^n and the orbit space M/(Z_2)^2 is a simple convex polytope. For instance, RP^n with a natural action of (Z_2)^2 is a small cover over an nsimplex. In general, real toric manifolds, the set of real points of a toric manifold, provide examples of small covers.
Hence we may think of small covers as a topological generalization of real toric manifolds in algebraic geometry. Small covers over hypercubes are known to be real Bott manifolds, which is obtained as iterated RP^1 bundles starting with a point, where each fibration is the projectivization of a Whitney sum of two real line bundles [Masuda and Panov]. Choi found the 11 correspondence between the set of real Bott manifolds and the set of acyclic digraphs in a previous work.


LINKS



FORMULA

Sum_{n>0} a(n)*x^n/(2^(n1)*x1)^(n+1) = x/(1x). [Vladeta Jovovic, Oct 24 2009]


MATHEMATICA

r[0] = r[1] = 1; r[n_] := r[n] = Sum[(1)^(k+1) Binomial[n, k] 2^(k(nk)) r[nk], {k, 1, n}];
a[1] = 1; a[n_] := Sum[(1)^(k+1) Binomial[n1, k] 2^((k1)(n1k)) r[n1k], {k, 1, n1}];


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



