Tootfinder

Filing: Google pushes back on Epic's demands following its antitrust win, says the proposed remedies are "unnecessary" and "far beyond the scope" of the verdict (Sarah Perez/TechCrunch)
https://techcrunch…

Google dubs Epic's demands from its antitrust win 'unnecessary' and 'far beyond the scope' of the verdict | TechCrunch
The new filing, along with Epic's proposal, will help to inform Judge James Donato in a hearing scheduled on May 23 about what actions to take next to put Google’s power in check.

Co-rank $1$ Arithmetic Siegel--Weil III: Geometric local-to-global
Ryan C. Chen
https://arxiv.org/abs/2405.01428 https://arxiv.org/pd…

Co-rank $1$ Arithmetic Siegel--Weil III: Geometric local-to-global
This is the third in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank $1$ for Kudla--Rapoport special cycles on exotic smooth integral models of unitary Shimura varieties of arbitrarily large even arithmetic dimension. Our arithmetic Siegel--Weil formula implies that degrees of Kudla--Rapoport arithmetic special $1$-cycles are encoded in the first derivatives of unitary Eisenstein series Fourier coefficients. In this paper, we finish the reduction proce…

This https://arxiv.org/abs/2402.15778 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Graphs with a given conditional diameter that maximize the Wiener index
The Wiener index $W(G)$ of a graph $G$ is one of the most well-known topological indices, which is defined as the sum of distances between all pairs of vertices of $G$. The diameter $D(G)$ of $G$ is the maximum distance between all pairs of vertices of $G$; the conditional diameter $D(G;s)$ is the maximum distance between all pairs of vertex subsets with cardinality $s$ of $G$. When $s=1$, the conditional diameter $D(G;s)$ is just the diameter $D(G)$. The authors in \cite{QS} characterized the …

This https://arxiv.org/abs/2302.00360 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Faster maximal clique enumeration in large real-world link streams
Link streams offer a good model for representing interactions over time. They consist of links $(b,e,u,v)$, where $u$ and $v$ are vertices interacting during the whole time interval $[b,e]$. In this paper, we deal with the problem of enumerating maximal cliques in link streams. A clique is a pair $(C,[t_0,t_1])$, where $C$ is a set of vertices that all interact pairwise during the full interval $[t_0,t_1]$. It is maximal when neither its set of vertices nor its time interval can be increased. S…

This https://arxiv.org/abs/2210.02779 has been replaced.
link: https://scholar.google.com/scholar?q=a

Nef cones of fiber products and an application to the Cone Conjecture
We prove a decomposition theorem for the nef cone of smooth fiber products over curves, subject to the necessary condition that their Néron--Severi space decomposes. We apply it to describe the nef cone of so-called Schoen varieties, which are the higher dimensional analogues of the Calabi--Yau threefolds constructed by Schoen. Schoen varieties give rise to Calabi--Yau pairs, and in each dimension at least three, there exist Schoen varieties with non-polyhedral nef cone. We prove the Kawamata-…

This https://arxiv.org/abs/2402.15778 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Graphs with a given conditional diameter that maximize the Wiener index
The Wiener index $W(G)$ of a graph $G$ is one of the most well-known topological indices, which is defined as the sum of distances between all pairs of vertices of $G$. The diameter $D(G)$ of $G$ is the maximum distance between all pairs of vertices of $G$; the conditional diameter $D(G;s)$ is the maximum distance between all pairs of vertex subsets with cardinality $s$ of $G$. When $s=1$, the conditional diameter $D(G;s)$ is just the diameter $D(G)$. The authors in \cite{QS} characterized the …

Growth of regular partitions 3: strong regularity and the vertex partition
C. Terry
https://arxiv.org/abs/2404.02024 https://arxiv.or…

Growth of regular partitions 3: strong regularity and the vertex partition
This is Part 3 in a series of papers about the growth of regular partitions in $3$-uniform hypergraphs. We consider here the strong regularity for $3$-uniform hypergraphs developed by Frankl, Gowers, Kohayakawa, Nagle, Rödl, Skokan, and Schacht. This type of regular decomposition comes with two components, a partition of vertices, and a partition of pairs of vertices. We define two corresponding growth functions associated to a hereditary property $\mathcal{H}$ of $3$-uniform hypergraphs: $T_{…

Growth of regular partitions 4: strong regularity and the pairs partition
C. Terry
https://arxiv.org/abs/2404.02030 https://arxiv.org…

Growth of regular partitions 4: strong regularity and the pairs partition
This is the fourth in a series of papers on the growth of regular partitions in $3$-uniform hypergraphs. In this paper, we consider a form of regularity for $3$-uniform hypergraphs which was developed by Frankl, Gowers, Kohayakawa, Nagle, Rödl, Skokan, and Schacht. Regular decompositions of this type involve two components, a partition on the vertex set and a partition on the pairs of vertices. To each hereditary property $\mathcal{H}$ of $3$-uniform hypergraphs, we associate two corresponding…

This https://arxiv.org/abs/2106.13372 has been replaced.
link: https://scholar.google.com/scholar?q=a

Graphs with Many Hamiltonian Paths
A graph is \emph{hamiltonian-connected} if every pair of vertices can be connected by a hamiltonian path, and it is \emph{hamiltonian} if it contains a hamiltonian cycle. We construct families of non-hamiltonian graphs for which the ratio of pairs of vertices connected by hamiltonian paths to all pairs of vertices approaches 1. We then consider minimal graphs that are hamiltonian-connected. It is known that any order-$n$ graph that is hamiltonian-connected must have $\geq 3n/2$ edges. We constr…

An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups
Sudip Bera, Hiranya Kishore Dey
https://arxiv.org/abs/2405.01027

An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups
The enhanced power graph of a group $G$ is a graph with vertex set $G,$ where two distinct vertices $x$ and $y$ are adjacent if and only if there exists an element $w$ in $G$ such that both $x$ and $y$ are powers of $w.$ In this paper, we determine the vertex connectivity of the enhanced power graph of any finite nilpotent group.