✦ LIBER ✦

A note on coloured quadrangulations

✍ Scribed by Kenneth A. Berman

Publisher: Elsevier Science
Year: 1980
Tongue: English
Weight: 175 KB
Volume: 29
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(80)90011-4

No coin nor oath required. For personal study only.

✦ Synopsis

Consider a quadrilateral drawn in the plane labelled ABCD counter-clockwise. Partition this quadrilateral into smaller quadrilaterals by selecting an even number of points (or no points) on each of the sides and any number of points in the interior. The resultant map is a planar quadrungulation, that is ti planar map such that each face has valency 4 except possibly the outside face. (See [I]). Label the points on the side AB alternately A and B. Similarly label the points on the other three sides alternately B aod C, C and D, D and A. Now, label the interior points in any way such that no two adjacent points (perimeter or interior) have the same label. Call the resultant coloured quadrangulation Q. There are 24 possible labellings of the small quadrilaterals, six of which use all four labels. In Fig. 1, an example of a coloured quadrangulation Q is given. Note that there is a small quadrilateral labelled ABCD counterclockwise.

The purpose of this note is to prove the following theorem.

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