Geodesic
On the generalized Chebyshev polynomials corresponding to plane trees of diameter~4
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 6, pp. 19-33

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{FPM_2007_13_6_a2,
     author = {N. M. Adrianov},
     title = {On the generalized {Chebyshev} polynomials corresponding to plane trees of diameter~4},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {19--33},
     publisher = {mathdoc},
     volume = {13},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a2/}
}
TY  - JOUR
AU  - N. M. Adrianov
TI  - On the generalized Chebyshev polynomials corresponding to plane trees of diameter~4
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2007
SP  - 19
EP  - 33
VL  - 13
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a2/
LA  - ru
ID  - FPM_2007_13_6_a2
ER  - 
%0 Journal Article
%A N. M. Adrianov
%T On the generalized Chebyshev polynomials corresponding to plane trees of diameter~4
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2007
%P 19-33
%V 13
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a2/
%G ru
%F FPM_2007_13_6_a2
N. M. Adrianov. On the generalized Chebyshev polynomials corresponding to plane trees of diameter~4. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 6, pp. 19-33. http://geodesic.mathdoc.fr/item/FPM_2007_13_6_a2/