Abstract
The equations of the title appear in the author's paper “Chromatic Sums for Rooted Planar Triangulations, V: Special Equations.” (Canadian Journal of Mathematics, 26 (1974), 893–907). They appear in that paper as Equations (24) and (25). They are simultaneous equations for two unknown functionsl andy2 of two variablesy1 andz. A parameterμ is involved. The main result is that forμ = 2 cos (2π/n), wheren is a positive integer >1, the two equations can be reduced to a single equation (numbered (49)). Solutions of this are known forn <7. From such solutions we can expect to get information about the averaged chromatic polynomials of planar triangulations with a given number of triangles.
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