A Census of Slicings

W. T. Tutte

doi:10.4153/CJM-1962-061-1

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A band is a closed connected set in the 2-sphere, bounded by one or more disjoint simple closed curves.

Consider a band B with bounding curves J1, J2, … , Jk. On each curve Ji let there be chosen mi ≥ 0 points to be called vertices, with the restriction that the sum of the k integers mi is to be even. Write

(1)

Next consider a set of n disjoint open arcs in the interior of B which join the 2n vertices in pairs and partition the remainder of the interior of B into simply connected domains. We call the resulting dissection of B a slicing with respect to the given set of vertices. The arcs are the internal edges of the slicing and the simply connected domains are its internal faces, or slices.

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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