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Working paper

On arithmetic of plane trees

math. arxive. Cornell University, 2017. No. 1711.03393.
In [3] L. Zapponi studied the arithmetic of plane bipartite trees with prime number of edges. He obtained a lower bound on the degree of tree's definition field. Here we obtain a similar lower bound in the following case. There exists a prime p such, that: a) the number of edges is divisible by p, but not by p2; b) for any proper subset of white (black) vertices the sum of their degrees is not divisible by this p.