Conditions on periodicity for sum-free sets.
We found that there is a remarkable relationship between the triangular numbers and the astronomical clock (horologe) of Prague. We introduce Šindel sequences of natural numbers as those periodic sequences with period that satisfy the following condition: for any there exists such that . We shall see that this condition guarantees a functioning of the bellworks, which is controlled by the horologe. We give a necessary and sufficient condition for a periodic sequence to be a Šindel sequence....
On caractérise les puissances -ièmes dans un corps quadratique réel et dans à l’aide des polynômes de Dickson. Ces mêmes polynômes sont utilisés pour obtenir des renseignements sur l’indice du groupe des unités d’un ordre non-maximal dans le groupe de toutes les unités d’un corps quadratique réel. Le texte est détaillé et élémentaire.
Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any ℓ ∈ N, maximal distance-ℓ independent (or simply: maximal ℓ-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied