

A156098


Number of rigid genus2 nonbipartite crystallizations of orientable 3manifolds with 2n vertices.


1



1, 1, 1, 1, 2, 2, 3, 2, 6, 7, 9, 7, 12, 12, 16
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OFFSET

7,5


COMMENTS

This is the lower row of Table 1, p.9, of Bandieri, et al. There are no rigid genus two crystallizations with less than 14 vertices (i.e., with n = 7). Abstract: "We improve and extend to the nonorientable case a recent result of Karabas, Malicki and Nedela concerning the classification of all orientable prime 3manifolds of Heegaard genus two, triangulated with at most 42 coloured tetrahedra." Karabas, Malicki and Nedela show that there exist exactly 78 nonhomeomorphic, closed, orientable, prime 3manifolds with Heegaard genus two, admitting a colored triangulation with at most 42 tetrahedra. Each manifold M is identified by a suitable 6tuple of nonnegative integers, representing a minimal crystallization  hence a minimal colored triangulation  of M. From such a 6tuple, a presentation of the fundamental group and of the first homology group of M are easily obtained.


LINKS

Table of n, a(n) for n=7..21.
Paola Bandieri, Paola Cristofori and Carlo Gagliardi, A census of genus two 3manifolds up to 42 coloured tetrahedra, Feb 3, 2009.
P. Bandieri et al., A census of genustwo 3manifolds [with] up to 42 colored tetrahedra, Discrete Math., 310 (2010), 24692481. [N. J. A. Sloane, Aug 26 2010]
J. Karabas, P. Malicky, R. Nedela, Threemanifolds with Heegaard genus at most two represented by crystallisations with at most 42 vertices, Discrete Math. 307 (2007), no. 21, 25692590.


CROSSREFS

A156097 enumerates all rigid bipartite examples.
Sequence in context: A095757 A144368 A094438 * A294933 A015996 A256564
Adjacent sequences: A156095 A156096 A156097 * A156099 A156100 A156101


KEYWORD

nonn,more


AUTHOR

Jonathan Vos Post, Feb 04 2009


EXTENSIONS

Edited by N. J. A. Sloane, Sep 26 2010


STATUS

approved



