11 citations · 16 across the 5 of their papers we have counts for
6 papers
Number systems and the Chinese Remainder Theorem
Christiaan E. van de Woestijne
A well-known generalisation of positional numeration systems is the case where the base is the residue class of modulo a given polynomial with coefficients in (for examp…
Factors of disconnected graphs and polynomials with nonnegative integer coefficients
Christiaan E. van de Woestijne
We investigate the uniqueness of factorisation of possibly disconnected finite graphs with respect to the Cartesian, the strong and the direct product. It is proved that if a graph…
Digit systems over commutative rings
Klaus Scheicher, Paul Surer, Jörg M. Thuswaldner +1
Let $\E$ be a commutative ring with identity and $P\in\E[x]$ be a polynomial. In the present paper we consider digit representations in the residue class ring $\E[x]/(P)$. In parti…
Exact solutions to Waring's problem for finite fields
Arne Winterhof, Christiaan van de Woestijne
The Waring function measures the difficulty of Waring's problem for th powers in the field of elements. Its calculation seems to be difficult, and many partial resu…
Noncanonical number systems in the integers
Christiaan van de Woestijne
The well known binary and decimal representations of the integers, and other similar number systems, admit many generalisations. Here, we investigate whether still every integer co…
The Casas-Alvero conjecture for infinitely many degrees
Hans-Christian Graf von Bothmer, Oliver Labs, Josef Schicho +1
Over a field of characteristic zero, it is clear that a polynomial of the form (X-a)^d has a non-trivial common factor with each of its d-1 first derivatives. The converse has been…