Abstract
The “true form” of plane trees, i.e., the geometry of sets p −1[0, 1], where p is a Chebyshev polynomial, is considered. Empiric data about the true form are studied and systematized.
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J. Bétréma, D. Péré, and A. Zvonkin, Plane Trees and Their Shabat Polynomials. Catalog, Technical Report LaBRI No. 92-75, Bordeaux (1992).
V. Dremov and Yu. Kochetkov, “Geometry of trees and Abelian integrals,” in: Problems of Group Theory and Homological Algebra, Yaroslavl’ (2003), pp. 61–74.
Yu. Yu. Kochetkov, “On the geometry of a class of plane trees,” Funkts. Anal. Prilozh., 33, No. 4, 78–81 (1999).
G. B. Shabat and A. K. Zvonkin, “Plane trees and algebraic numbers,” in: H. Barcelo and G. Kalai, eds., Jerusalem Combinatorics ’93, Contemp. Math., Vol. 178, Amer. Math. Soc. (1994), pp. 233–275.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 6, pp. 149–158, 2007.
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Kochetkov, Y.Y. Geometry of plane trees. J Math Sci 158, 106–113 (2009). https://doi.org/10.1007/s10958-009-9376-4
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DOI: https://doi.org/10.1007/s10958-009-9376-4