%I A156097
%S A156097 1,2,4,6,8,14,18,23,38,47,58,79,118,128,159
%N A156097 Number of genus-two rigid bipartite crystallizations with 2n vertices.
%C A156097 This is the upper row of Table 1, p.9, of Bandieri, et al. We point out 
               that there are no rigid genus two crystallizations with less than 
               14 vertices (i.e. with n = 7). Abstract: "We improve and extend to 
               the non-orientable case a recent result of Karabas, Malicki and Nedela 
               concerning the classification of all orientable prime 3-manifolds 
               of Heegaard genus two, triangulated with at most 42 coloured tetrahedra." 
               Karabas, Malicki and Nedela show that there exist exactly 78 non-homeomorphic, 
               closed, orientable, prime 3-manifolds with Heegaard genus two, admitting 
               a coloured triangulation with at most 42 tetrahedra. Each manifold 
               M is identified by a suitable 6-tuple of non-negative integers, representing 
               a minimal crystallization - hence a minimal coloured triangulation 
               - of M. From such a 6-tuple, a presentation of the fundamental group 
               and of the first homology group of M are easily obtained.
%D A156097 J. Karabas, P. Malicky, R. Nedela, Three-manifolds with Heegaard genus 
               at most two represented by crystallisations with at most 42 vertices, 
               Discrete Math. 307 (2007), no. 21, 2569-2590.
%H A156097 Paola Bandieri, Paola Cristofori and Carlo Gagliardi, <a href="http:/
               /arxiv.org/abs/0902.0492">A census of genus two 3-manifolds up to 
               42 coloured tetrahedra</a>, Feb 3, 2009.
%Y A156097 Sequence in context: A049015 A005250 A162762 this_sequence A039597 A000937 
               A167229
%Y A156097 Adjacent sequences: A156094 A156095 A156096 this_sequence A156098 A156099 
               A156100
%K A156097 nonn
%O A156097 7,2
%A A156097 Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 04 2009