Tootfinder

@… is someone who has done more than most to help her compatriots in this dreadful #GazaGenocide. To see her express such despair breaks my heart.
There must be rebuilding.
There must be reparations.
Palestine must be free.
There is no pea…

Finding arithmetic progressions in dense sets of integers
Sarah Peluse
https://arxiv.org/abs/2509.22962 https://arxiv.org/pdf/2509.22962

Finding arithmetic progressions in dense sets of integers
One of the central problems in additive combinatorics is to determine how large a subset of the first $N$ integers can be before it is forced to contain $k$ elements forming an arithmetic progression. Around 25 years ago, Gowers proved the first reasonable upper bounds in this problem for progressions of length four and longer. In this work, Gowers initiated the study of "higher-order Fourier analysis", which has developed over the past couple of decades into a rich theory with numerous other c…

Hovering Sets in Near Pseudo-Integrable Hamiltonian Impact Systems
Idan Pazi, Alexandra Zobova, Vered Rom-Kedar
https://arxiv.org/abs/2509.24688 https://ar…

Hovering Sets in Near Pseudo-Integrable Hamiltonian Impact Systems
The transition from rotational to discontinuous behavior of the return map of the perturbed oscillators-step system, a paradigm model for a perturbation of a pseudo-integrable Hamiltonian impact system, is studied. The form of the return map is derived, and a truncated form of this map is simulated and analyzed. For a set of parameters the existence of a hovering set, a set of non-resonant orbits that pass sometimes above the step and sometimes to its side, without ever impacting it, is establi…