Tootfinder

List coloring ordered graphs with forbidden induced subgraphs
Marta Piecyk, Pawe{\l} Rz\k{a}\.zewski
https://arxiv.org/abs/2509.22160 https://arxiv.org/pdf…

List coloring ordered graphs with forbidden induced subgraphs
In the List $k$-Coloring problem we are given a graph whose every vertex is equipped with a list, which is a subset of $\{1,\ldots,k\}$. We need to decide if $G$ admits a proper coloring, where every vertex receives a color from its list. The complexity of the problem in classes defined by forbidding induced subgraphs is a widely studied topic in algorithmic graph theory. Recently, Hajebi, Li, and Spirkl [SIAM J. Discr. Math. 38 (2024)] initiated the study of List $3$-Coloring in ordered grap…

Constructions of Compact Dupin Hypersurfaces with Non-constant Lie Curvatures
Thomas E. Cecil
https://arxiv.org/abs/2509.21235 https://arxiv.org/pdf/2509.2…

Constructions of Compact Dupin Hypersurfaces with Non-constant Lie Curvatures
A hypersurface $M$ in the unit sphere $S^n \subset {\bf R}^{n+1}$ is Dupin if along each curvature surface of $M$, the corresponding principal curvature is constant. If the number $g$ of distinct principal curvatures is constant on $M$, then $M$ is called proper Dupin. In this expository paper, we give a detailed description of two important types of constructions of compact proper Dupin hypersurfaces in $S^n$. One construction was published in 1989 by Pinkall and Thorbergsson, and the second w…

On Tent Spaces for the Gaussian Measure
Liliana Forzani, Roberto Scotto, Wilfredo Urbina
https://arxiv.org/abs/2509.16148 https://arxiv.org/pdf/2509.16148

On Tent Spaces for the Gaussian Measure
Following the scheme of tent spaces in classical harmonic analysis developed by R. Coifman, Y. Meyer, and E. Stein in \cite{cms}, we succeed in doing so for the Gaussian setting. In \cite{MNP}, part of this theory (an atomic decomposition) is developed for a specific tent space where functions are defined just in a proper subset of $\mathbb{R}^{n+1}_+,$ and without the use of an area function. In the present paper, using a variation of the area function considered in \cite{FSU}, we define the G…

A spectral condition for Hamilton cycles in tough bipartite graphs
Lianyang Ai, Wenqian Zhang
https://arxiv.org/abs/2508.03778 https://arxiv.org/pdf/2508.0…

A spectral condition for Hamilton cycles in tough bipartite graphs
Let $G$ be a graph. The {\em spectral radius} of $G$ is the largest eigenvalue of its adjacency matrix. For a non-complete bipartite graph $G$ with parts $X$ and $Y$, the {\em bipartite toughness} of $G$ is defined as $t^{B}(G)=\min\left\{\frac{|S|}{c(G-S)}\right\}$, where the minimum is taken over all proper subsets $S\subset X$ (or $S\subset Y$) such that $c(G-S)>1$. In this paper, we give a sharp spectral radius condition for balanced bipartite graphs $G$ with $t^{B}(G)\geq1$ to gu…

Modular fusion categories with few twists
Andrew Schopieray
https://arxiv.org/abs/2509.02501 https://arxiv.org/pdf/2509.02501

Modular fusion categories with few twists
We classify modular fusion categories up to braided equivalence with less than four distinct twists of simple objects by observing that under this assumption, for each positive integer $N$, there are finitely many modular fusion categories of Frobenius-Schur exponent $N$ up to braided equivalence whose twists are a proper subset of the $N^\mathrm{th}$ roots of unity.

Is Quantum Mechanics a proper subset of Classical Mechanics?
Khaled Mnaymneh
https://arxiv.org/abs/2508.00044 https://arxiv.org/pdf/2508.00044

Is Quantum Mechanics a proper subset of Classical Mechanics?
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the Hamilton type 1 principal function, we show that classical action-based dynamics are generally undecidable, paralleling spectral gap undecidability in quantum systems. In near Kolmogorov-Arnold-Moser systems, stability hinges on Diophantine conditions that are…