Tootfinder

This https://arxiv.org/abs/2405.05902 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The largest subgraph without a forbidden induced subgraph
We initiate the systematic study of the following Turán-type question. Suppose $Γ$ is a graph with $n$ vertices such that the edge density between any pair of subsets of vertices of size at least $t$ is at most $1 - c$, for some $t$ and $c > 0$. What is the largest number of edges in a subgraph $G \subseteq Γ$ which does not contain a fixed graph $H$ as an induced subgraph or, more generally, which belongs to a hereditary property $\mathcal{P}$? This provides a common generalization of two r…

On Fukaya categories and prequantization bundles
Tatsuki Kuwagaki, Adrian Petr, Vivek Shende
https://arxiv.org/abs/2406.08852 https://

On Fukaya categories and prequantization bundles
We show: the Floer homology of (nonexact!) integral Lagrangians in an (nonexact!) integral symplectic manifold can be computed in terms of exact Lagrangians in an exact filling of the prequantization bundle. As a consequence, we deduce a comparison to microsheaves. Throughout we work over the Novikov ring.

Eigenvalues of the Hodge Laplacian on digraphs
Alexander Grigor'yan, Yong Lin, S. -T. Yau, Haohang Zhang
https://arxiv.org/abs/2406.09814 https://

Eigenvalues of the Hodge Laplacian on digraphs
This paper aims to compute and estimate the eigenvalues of the Hodge Laplacians on directed graphs. We have devised a new method for computing Hodge spectra with the following two ingredients. (I) We have observed that the product rule does work for the so-called normalized Hodge operator, denoted by $Δ_{p}^{(a)},$ where $a$ refers to the weight that is used to redefine the inner product in the spaces $Ω_{p}$. This together with the Künneth formula for product allows us to compute inductiv…