arXiv:2607. 24847v1 Announce Type: cross Abstract: We introduce an extremal invariant associated with Chowla-type order conditions in finite groups.
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arXiv:2607. 23732v1 Announce Type: cross Abstract: In Question~3.
arXiv:2608. 07275v1 Announce Type: cross Abstract: A group is an E-group if every element commutes with each of its endomorphic images.
arXiv:2607. 23004v1 Announce Type: cross Abstract: Let $t(N)$ be the largest $t$ for which there exist distinct sets $A_1,\dots,A_t \subseteq \{1,\dots,N\}$ such that $A_i \cap A_j$ is a nonempty arithmetic progression for all $i \neq j$ (Erdos Problem #272).
arXiv:2603. 20861v2 Announce Type: replace-cross Abstract: The homology of an ample groupoid is computed from the complex of compactly supported continuous functions on the nerve.
arXiv:2608. 15558v1 Announce Type: cross Abstract: For $m\geq 2$, let $c_p(m)$ be the all-dimensional best constant in $$ \left\|\sum_{k=1}^m A_k\right\|_p \leq c_p(m)\left\|\sum_{k=1}^m |A_k|\right\|_p.
arXiv:2607. 10751v1 Announce Type: new Abstract: Following Alon, Hanneke, Holzman, and Moran (FOCS 2021), we define a partial concept class (PCC) as a family of partial functions \(f: V\to\{0,1,\ast\}\); equivalently, its concepts partition the ground set into black ($f^{-1}(1)$), grey ($f^{-1}(\ast)$), and white parts ($f^{-1}(0)$).