Tootfinder

This https://arxiv.org/abs/2410.13695 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Zarankiewicz bounds from distal regularity lemma
Since Kővári, Sós, and Turán proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricting to particular classes of graphs. In 2017, Fox, Pach, Sheffer, Suk, and Zahl proved better bounds for semialgebraic binary relations, and this work was extended by Do in the following year to arbitrary semialgebraic relations. In this paper, we show that Zarankiewicz bounds in the shape of Do's are enjoyed by all re…

Next stop on our NLP timeline (as part of the #ISE2025 lecture) was Terry Winograd's SHRDLU, an early natural language understanding system developed in 1968-70 that could manipulate blocks in a virtual world.
Winograd, T. Procedures as a Representation for Data in a Computer Program for Understanding Natural Language. MIT AI Technical Report 235.

Rumors on evolving graphs through stationary times
Vicenzo Bonasorte
https://arxiv.org/abs/2506.04386 https://arxiv.org/pdf/2506.0438…

Rumors on evolving graphs through stationary times
We study rumor spreading in dynamic random graphs. Starting with a single informed vertex, the information flows until it reaches all the vertices of the graph (completion), according to the following process. At each step $k$, the information is propagated to neighbors of the informed vertices, in the $k$-th generated random graph. The way this information propagates from vertex to vertex at each step will depend on the ``protocol". We provide a method based on strong stationary times to study…

This https://arxiv.org/abs/2504.21059 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A remark on the number of automorphisms of some algebraic structures
In these notes we look at the following question. Given a category $\mathcal C$ of algebraic structure (e.g. the category of groups, monoids, partial groups, ...) and a rational $r\in \mathbb Q$, does there exists an element $x\in \mathcal C$ such that the size of its automorphism group $\text{Aut}_{\mathcal C} (x)$ divided by the size of $x$ (whatever that would means) is equal to $r$\,? To our knowledge, this question was introduced by Tărnăuceanu in the category of groups. Here, we answer …

The stability of independence polynomials of complete bipartite graphs
Guo Chen, Bo Ning, Jianhua Tu
https://arxiv.org/abs/2505.24381 https://

The stability of independence polynomials of complete bipartite graphs
The independence polynomial of a graph is termed {\it stable} if all its roots are located in the left half-plane $\{z \in \mathbb{C} : \mathrm{Re}(z) \leq 0\}$, and the graph itself is also referred to as stable. Brown and Cameron (Electron. J. Combin. 25(1) (2018) \#P1.46) proved that the complete bipartite graph $K_{1,n}$ is stable and posed the question: \textbf{Are all complete bipartite graphs stable?} We answer this question by establishing the following results: \begin{itemize} \i…

Localized atomic vibrations caused by point impurity in long chains of noble gas atoms adsorbed in outer grooves of carbon nanobundle
E. V. Manzhelii, S. B. Feodosyev
https://arxiv.org/abs/2505.24497

Localized atomic vibrations caused by point impurity in long chains of noble gas atoms adsorbed in outer grooves of carbon nanobundle
The characteristics of discrete vibrational levels caused by a point three-parameter substitutional impurity in long linear chain of inert gas atoms adsorbed in groove on the surface of carbon nanobundle are studied. The impurity atom differs from the atoms of the chain in the following parameters: the mass, the parameter of interaction with neighboring atoms and the parameter of interaction with the substrate. Analytical expressions for the frequencies of the localized vibrations and the inten…

Hausdorff Dimension of non-conical and Myrberg limit sets
Mahan Mj, Wenyuan Yang
https://arxiv.org/abs/2506.04955 https://arxiv.org/p…

Hausdorff Dimension of non-conical and Myrberg limit sets
In this paper, we develop techniques to study the Hausdorff dimensions of non-conical and Myrberg limit sets for groups acting on negatively curved spaces. We establish maximality of the Hausdorff dimension of the non-conical limit set of $G$ in the following cases. 1. $M$ is a finite volume complete Riemannian manifold of pinched negative curvature and $G$ is an infinite normal subgroups of infinite index in $π_1(M)$. 2. $G$ acts on a regular tree $X$ with $X/G$ infinite and amenable (dimensi…

Cardinalities of the total number of independent sets
Benedek Kov\'acs, Zolt\'an L\'or\'ant Nagy
https://arxiv.org/abs/2505.24794 https://

Cardinalities of the total number of independent sets
We study the set of numbers the total number of independent sets can admit in $n$-vertex graphs. In this paper, we prove that the cardinality of this set $\mathcal{N}i(n)$ is very close to $2^n$ in the following sense: $\mathcal{N}i(n)/2^n = O(n^{-1/5})$ while for infinitely many $n$, we have $\log_2(\mathcal{N}i(n)/2^n)\ge -2^{(1+o(1)\sqrt{\log_2 n}}$. This set is also precisely the set of possible values of the independence polynomial $I_G(x)$ at $x=1$ for $n$-vertex graphs $G$. As an applica…