Chebyshev Polynomials, Zolotarev Polynomials, and Plane Trees
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| 024 | 7 | 0 | |a 10.1007/s10958-015-2502-6 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10958-015-2502-6 | ||
| 100 | 1 | |a Kochetkov |D Yu |u Higher School of Economics, Moscow, Russia |4 aut | |
| 245 | 1 | 0 | |a Chebyshev Polynomials, Zolotarev Polynomials, and Plane Trees |h [Elektronische Daten] |c [Yu. Kochetkov] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media New York, 2015 | ||
| 773 | 0 | |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 209/2(2015-08-01), 275-281 |x 1072-3374 |q 209:2<275 |1 2015 |2 209 |o 10958 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10958-015-2502-6 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10958-015-2502-6 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Kochetkov |D Yu |u Higher School of Economics, Moscow, Russia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Mathematical Sciences |d Springer US; http://www.springer-ny.com |g 209/2(2015-08-01), 275-281 |x 1072-3374 |q 209:2<275 |1 2015 |2 209 |o 10958 | ||