# A note on the paper arXiv:2207.13335

no code yet • 2 Aug 2022

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

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# A quantitative and constructive proof of Willems' Fundamental Lemma and its implications

no code yet • 1 Aug 2022

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

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# Semi-algebraic and semi-linear Ramsey numbers

no code yet • 1 Aug 2022

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

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# Small resolutions of special three-dimensional varieties

no code yet • 2 Aug 2022

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

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# On the history of Lie brackets, crossed modules, and Lie-Rinehart algebras

no code yet • 4 Aug 2022

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)

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# Quadratis Puzzles

no code yet • 2 Aug 2022

We introduce a family of reconfiguration puzzles arising from ideas in geometry and topology.

Geometric Topology Combinatorics History and Overview

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# Pure Braid Group Presentations via Longest Elements

no code yet • 3 Aug 2022

This paper gives a new, simplified presentation of the classical pure braid group.

Group Theory Algebraic Geometry

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# Topology of irregular isomonodromy times on a fixed pointed curve

no code yet • 4 Aug 2022

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

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# The invariants of the Weil representation of $\mathrm{SL}_2(\mathbb{Z})$

no code yet • 3 Aug 2022

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

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# Jacobi forms with CM and applications

no code yet • 3 Aug 2022

We define Jacobi forms with complex multiplication.

Number Theory 11F50

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