Chromatic Sums for Rooted Planar Triangulations, III: The Case λ = 3

Abstract

SummaryIn this paper we are chiefly concerned with the chromatic sums we have called l and h, with colour-number 3. In this case h can be interpreted as enumerating the rooted Eulerian triangulations with a given number of faces, and l as enumerating such triangulations with a given number of faces and a given valency for the root-vertex. The series h has been determined already, by summation from the formula enumerating even slicings [3]. However our formula for l does not seem to have been published before, though it could presumably be derived in a similar way.