6 papers
A Fibonacci type sequence with Prouhet-Thue-Morse coefficients
Eryk Lipka, Maciej Ulas
Let , where is the sum of binary digits function. The sequence is the well-known Prouhet-Thue-Morse sequence. In this note we…
Detecting a single fault in a deterministic finite automaton
Artur Polański, Eryk Lipka
Given a deterministic finite automaton and its implementation with at most one single fault, that we can test on a set of inputs, we provide an algorithm to find a test set that gu…
On two conjectures regarding generalized sequence of derangements
Eryk Lipka, Piotr Miska
The second author studied arithmetic properties of a class of sequences that generalize the sequence of derangements. The aim of the following paper is to disprove two conjectures…
A note on minimal art galleries
Eryk Lipka
We will consider some extensions of the polygonal art gallery problem. In a recent paper Morrison has shown the smallest (9 sides) example of an art gallery that cannot be observed…
Further improving of upper bound on a geometric Ramsey problem
Eryk Lipka
We consider following geometric Ramsey problem: find the least dimension such that for any 2-coloring of edges of complete graph on the points there exists 4-vert…
Automaticity of the sequence of the last nonzero digits of in a fixed base
Eryk Lipka
In 2011 Deshouillers and Ruzsa tried to argument that the sequence of the last nonzero digit of in base 12 is not automatic. This statement was proved few years later by Desho…