Summary
This paper discusses some equations arising in the author's work on “chromatic sums”. The main results were presented in a series of papers extending from 1973 to 1982. The object here is to give a unified and simplified account of the elimination of unwanted variables from the initial equation, leading to the final identification of the desired chromatic sums as the coefficients in a power series satisfying a certain differential equation.
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References
Beraha, S.,Private communication.
Tutte, W. T.,A census of planar triangulations, Canad. J. Math.16 (1962), 21–38.
Tutte, W. T.,Chromatic sums for rooted planar triangulations; the cases λ = 1 and λ = 2. Canad. J. Math.25 (1973), 426–447.
Tutte, W. T.,Chromatic sums for rooted planar triangulations II; the case λ = τ + 1. Canad. J. Math.25 (1973), 657–671.
Tutte, W. T.,Chromatic sums for rooted planar triangulations III; the case λ = 3. Canad. J. Math.25 (1973), 780–790.
Tutte, W. T.,Chromatic sums for rooted planar triangulations IV; the case λ = ∞. Canad. J. Math.25 (1973), 929–940.
Tutte, W. T.,Chromatic sums for rooted planar triangulations V; special equations. Canad. J. Math.26 (1974), 893–907.
Tutte, W. T.,On a pair of functional equations of combinatorial interest. Aequationes Math.17 (1978), 121–140.
Tutte, W. T.,Chromatic solutions. Canad. J. Math.34 (1982), 741–758.
Tutte, W. T.,Chromatic solutions II. Canad. J. Math.34 (1982), 952–960.
Tutte, W. T.,The matrix of chromatic joins. J. Combin. Theory Ser. B57 (1993), 269–288.
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Tutte, W.T. Chromatic sums revisited. Aeq. Math. 50, 95–134 (1995). https://doi.org/10.1007/BF01831115
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DOI: https://doi.org/10.1007/BF01831115