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@arXiv_mathNT_bot@mastoxiv.page
2024-03-11 08:38:34

This https://arxiv.org/abs/2401.10821 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On integer distance sets
We develop a new approach to address some classical questions concerning the size and structure of integer distance sets. Our main result is that any integer distance set in the Euclidean plane has all but a very small number of points lying on a single line or circle. From this, we deduce a near-optimal lower bound on the diameter of any non-collinear integer distance set of size $n$ and a strong upper bound on the size of any integer distance set in $[-N,N]^2$ with no three points on a line a…

@arXiv_mathAG_bot@mastoxiv.page
2024-04-11 08:35:57

This https://arxiv.org/abs/2208.01517 has been replaced.
link: https://scholar.google.com/scholar?q=a

Derived $F$-zips
We define derived versions of $F$-zips and associate a derived $F$-zip to any proper, smooth morphism of schemes in positive characteristic. We analyze the stack of derived $F$-zips and certain substacks. We make a connection to the classical theory and look at problems that arise when trying to generalize the theory to derived $G$-zips and derived $F$-zips associated to lci morphisms. As an application, we look at Enriques-surfaces and analyze the geometry of the moduli stack of Enriques-surfa…

@arXiv_mathCO_bot@mastoxiv.page
2024-04-11 08:37:40

This https://arxiv.org/abs/2404.04502 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The interplay between additive and symmetric large sets and their combinatorial applications
The study of symmetric structures is a new trend in Ramsey theory. Recently Di Nasso introduced a systematic study of symmetrization of classical Ramsey theoretical results and proved a symmetric version of several Ramsey theoretic results. In this paper Di Nasso asked if his method could be adapted to find new non-linear Diophantine equations that are partition regular. By analyzing additive, multiplicative, and symmetric large sets, we construct new partition regular equations that give a fir…

@arXiv_csLO_bot@mastoxiv.page
2024-03-11 07:21:52

Superposition with Delayed Unification
Ahmed Bhayat, Johannes Schoisswohl, Michael Rawson
https://arxiv.org/abs/2403.04775 https://ar…

Superposition with Delayed Unification
Classically, in saturation-based proof systems, unification has been considered atomic. However, it is also possible to move unification to the calculus level, turning the steps of the unification algorithm into inferences. For calculi that rely on unification procedures returning large or even infinite sets of unifiers, integrating unification into the calculus is an attractive method of dovetailing unification and inference. This applies, for example, to AC-superposition and higher-order supe…

@arXiv_mathAG_bot@mastoxiv.page
2024-04-11 08:35:57

This https://arxiv.org/abs/2208.01517 has been replaced.
link: https://scholar.google.com/scholar?q=a

Derived $F$-zips
We define derived versions of $F$-zips and associate a derived $F$-zip to any proper, smooth morphism of schemes in positive characteristic. We analyze the stack of derived $F$-zips and certain substacks. We make a connection to the classical theory and look at problems that arise when trying to generalize the theory to derived $G$-zips and derived $F$-zips associated to lci morphisms. As an application, we look at Enriques-surfaces and analyze the geometry of the moduli stack of Enriques-surfa…