FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2007, VOLUME 13, NUMBER 6, PAGES 19-33

**On the generalized Chebyshev polynomials corresponding to plane trees
of diameter $4$**

N. M. Adrianov

Abstract

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The combinatorial classification of plane trees by the number of
realizations of their valency sets has distinguished some special
classes of plane trees.
One of them, the plane trees of diameter 4, turned out to be
a very interesting object of investigation from the Galois action
point of view.
In this paper, we present equation sets for some subclasses of trees
of diameter 4, calculate discriminants of the corresponding
generalized Chebyshev polynomials, some related polynomials, and their
fields of definitions, and use this to get some information about the
Galois action on plane trees.

Location: http://mech.math.msu.su/~fpm/eng/k07/k076/k07602h.htm

Last modified: April 22, 2008