6 citations · 19 across the 7 of their papers we have counts for
7 papers
Dependence of Homogeneous Components of Polynomials with Small Degree of Poisson Bracket
Daria Holik, Marek Karaś
Let F,G in C[x_1,...,x_n] be two polynomials in n variables x_1,...,x_n over the complex numbers field C. In this paper, we prove that if the degree of the Poisson bracket [F,G] is…
Wild multidegrees of the form (d,d_2,d_3) for given d greather than or equal to 3
Marek Karaś, Jakub Zygadło
Let d be any number greather than or equal to 3. We show that the intersection of the set mdeg(Aut(C^3))\ mdeg(Tame(C3)) with {(d_1,d_2,d_3) : d=d_1 =< d_2 =< d_3} has infinitely m…
Multidegrees of tame automorphisms of C^n
Marek Karaś
Let F=(F_1,...,F_n):C^n --> C^n be a polynomial mapping. By the multidegree of the mapping F we mean mdeg F=(deg F_1,...,deg F_n), an element of N^n. The aim of this paper is to st…
There is no tame automorphism of C^3 with multidegree (4,5,6)
Marek Karas
It is known that not each triple (d_1,d_2},d_3) of positive integers is a multidegree of a tame automorphism of C^3. In this paper we show that there is no tame automorphism of C^3…
Tame automorphisms of C^3 with multidegree of the form (3,d_2,d_3)
Marek Karas
In this note we prove that the sequence (3,d_2,d_3), where d_3>= d_2>= 3, is the multidegee of some tame automorphism of C^3, if and only if 3|d_2 or d_3 is a linaer combination of…
Tame automorphisms of C^3 with multidegree of the form (p_1,p_2,d_3)
Marek Karaś
Let d_3 >= p_2 > p_1 >= 3 be integers such that p_1,p_2 are prime numbers. In this paper we show that the sequence (p_1,p_2,d_3) is the multidegree of some tame automorphisms of C^…
There is no tame automorphism of C^3 with muldidegree (3,4,5)
Marek Karaś
Let F=(F_1,...,F_n):C^n --> C^n be any polynomial mapping. By multidegree of F, denoted mdeg F, we call the sequence of positive integers (deg F_1,...,F_n). In this paper we addres…