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A note on the paper arXiv:2207.13335
We show that all of the "new" permutation polynomials in the recent paper arXiv:2207. 13335 (H. Song et al.) are in fact known.
Number Theory 11T06
A quantitative and constructive proof of Willems' Fundamental Lemma and its implications
Willems' Fundamental Lemma provides a powerful data-driven parametrization of all trajectories of a controllable linear time-invariant system based on one trajectory with persistently exciting (PE) input.
Optimization and Control Systems and Control Systems and Control
Semi-algebraic and semi-linear Ramsey numbers
An $r$-uniform hypergraph $H$ is semi-algebraic of complexity $\mathbf{t}=(d, D, m)$ if the vertices of $H$ correspond to points in $\mathbb{R}^{d}$, and the edges of $H$ are determined by the sign-pattern of $m$ degree-$D$ polynomials.
Combinatorics
Small resolutions of special three-dimensional varieties
This is an English translation of Werner's 1987 dissertation "Kleine Aufl\"osungen spezieller dreidimensionaler Variet\"aten," originally published as Bonner Mathematische Schriften No.
Algebraic Geometry
On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras
The aim here is to sketch the development of ideas related to brackets and similar concepts: Some purely group theoretical combinatorics due to Ph.
History and Overview Algebraic Topology Differential Geometry Group Theory 01A60, 17B66, 18G45 (Primary) 12G05, 12H05, 17-03, 17B55, 20J05, 53-03, 53D17, 55Q15, 58H05 (Secondary)
Quadratis Puzzles
We introduce a family of reconfiguration puzzles arising from ideas in geometry and topology.
Geometric Topology Combinatorics History and Overview
Pure Braid Group Presentations via Longest Elements
This paper gives a new, simplified presentation of the classical pure braid group.
Group Theory Algebraic Geometry
Topology of irregular isomonodromy times on a fixed pointed curve
We will define and study moduli spaces of deformations of irregular classes on Riemann surfaces, which provide an intrinsic viewpoint on the "times" of irregular isomonodromy systems in general.
Algebraic Geometry Group Theory Geometric Topology 20F55, 20F36, 55R10
The invariants of the Weil representation of $\mathrm{SL}_2(\mathbb{Z})$
The transformation behaviour of the vector valued theta function of a positive definite even lattice under the metaplectic group $\mathrm{Mp}_2(\mathbb{Z})$ is described by the Weil representation.
Number Theory
Jacobi forms with CM and applications
We define Jacobi forms with complex multiplication.
Number Theory 11F50
