This paper concerns a class of combinatorial objects called Skolem starters, and more specifically, strong Skolem starters, which are generated by Skolem sequences. In 1991, Shalaby conjectured that any additive group
Z
n, where
n
≡
1 or
30.3em
(
mod0.3em
8
)
,0.33em
n
≥
11, admits a strong Skolem starter and constructed these starters of all admissible orders
11
≤
n
≤
57. Only finitely many strong Skolem starters have been known to date. In this paper, we offer a geometrical interpretation of strong Skolem starters and explicitly construct infinite families of them.
Undergraduate mathematics programmes in Europe are typically delivered in hierarchical structures of modules whose contents are in general assumed to be quite similar across universities. These programmes and the mechanisms through which they are maintained, revised and developed, have so far not been the subject of systematic research, as most research (including interventionbased research) takes the programme for granted. This paper furnishes a theoretical and methodological framework for undertaking didactic research in this area and provides some results from a first study in four universities in Denmark,
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.