arXiv subjects
Publications and source records attributed to Pascal Stumpf.
We study the monotonicity behavior of three slightly differently defined additive representation functions (as initiated by Erd\H{o}s, S\'{a}rk\"{o}zy and S\'{o}s), answering one open question and another one partially, and give a slightly simpler proof for a result of Chen and Tang.
We investigate a descent on simple graphs, starting with the complete graph on $n$ vertices and ending up with the cycle graph by removing one edge after another. We obtain quantitative results showing that graphs with large diameter must have some eigenvalues of large algebraic degree.
We solve a problem due to Recam\'an about the lower bound behavior of the maximum possible length among all arithmetic progressions in the least reduced residue system modulo $n$, as $n \to \infty$.