caa a22 4500 605526230 CHVBK 20210128100802.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10958-015-2502-6 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2502-6 Kochetkov Yu Higher School of Economics, Moscow, Russia aut Chebyshev Polynomials, Zolotarev Polynomials, and Plane Trees [Elektronische Daten] [Yu. Kochetkov] A polynomial with exactly two critical values is called a generalized Chebyshev polynomial (or Shabat polynomial). A polynomial with exactly three critical values is called a Zolotarev polynomial. Two Chebyshev polynomials f and g are called Z-homotopic if there exists a family pα, α ϵ $$ \epsilon $$ [0, 1], where p0 = f, p1 = g, and pα is a Zolotarev polynomial if α ϵ $$ \epsilon $$ (0, 1). As each Chebyshev polynomial defines a plane tree (and vice versa), Z-homotopy can be defined for plane trees. In this work, we prove some necessary geometric conditions for the existence of Z-homotopy of plane trees, describe Z-homotopy for trees with five and six edges, and study one interesting example in the class of trees with seven edges. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/2(2015-08-01), 275-281 1072-3374 209:2<275 2015 209 10958 https://doi.org/10.1007/s10958-015-2502-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2502-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kochetkov Yu Higher School of Economics, Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/2(2015-08-01), 275-281 1072-3374 209:2<275 2015 209 10958