12 citations · 22 across the 7 of their papers we have counts for
7 papers
On a Diophantine equation of Erdős and Graham
Szabolcs Tengely, Maciej Ulas, Jakub Zygadło
We study solvability of the Diophantine equation \begin{equation*} \frac{n}{2^{n}}=\sum_{i=1}^{k}\frac{a_{i}}{2^{a_{i}}}, \end{equation*} in integers sa…
On path sequences of graphs
Sławomir Bakalarski, Jakub Zygadło
A subset of vertices of a graph is called a -path vertex cover if every path on vertices in contains at least one vertex from . Denote by the m…
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…
On multidegree of tame and wild automorphisms of C^3
Marek Karas, Jakub Zygadlo
In this note we show that the set mdeg(Aut(C^3)) mdeg(Tame(C^3)) is not empty. Moreover we show that this set has infinitely many elements. Since for the famous Nagata's example N…
On multidegrees of polynomial automorphisms of C^3
Jakub Zygadło
We prove that for every pair of positive integers a, b there exists a number c_0 such that for every c>=c_0 one can find a tame polynomial automorphism of C^3 with multidegree equa…
Remarks on a normal subgroup of GA_n
Jakub Zygadło
We show that the subgroup generated by locally finite polynomial automorphisms of k^n is normal in GA_n. Also, some properties of normal subgroups of GA_n containing all diagonal a…
Minimal polynomial of an exponential automorphism of C^n
Jakub Zygadło
We show that the minimal polynomial of a polynomial exponential automorphism F of C^n (i.e. F=exp(D), where D is a locally nilpotent derivation) is of the form μ_F(T)=(T-1)^d, d=mi…