Tootfinder

This https://arxiv.org/abs/2203.09395 has been replaced.
link: https://scholar.google.com/scholar?q=a

Zero-sum partitions of Abelian groups and their applications to magic-type labelings
The following problem has been known since the 80s. Let $Γ$ be an Abelian group of order $m$ (denoted $|Γ|=m$), and let $t$ and $\{m_i\}_{i=1}^{t}$, be positive integers such that $\sum_{i=1}^t m_i=m-1$. Determine when $Γ^*=Γ\setminus\{0\}$, the set of non-zero elements of $Γ$, can be partitioned into disjoint subsets $\{S_i\}_{i=1}^{t}$ such that $|S_i|=m_i$ and $\sum_{s\in S_i}s=0$ for every $1 \leq i \leq t$. Such a subset partition is called a \textit{zero-sum parti…

A computational study of cutting-plane methods for multi-stage stochastic integer programs
Akul Bansal, Simge K\"u\c{c}\"ukyavuz
https://arxiv.org/abs/2405.02533

A computational study of cutting-plane methods for multi-stage stochastic integer programs
We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders', (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer L-shaped cuts correspond to one of the optimal solutions of the Lagrangian dual problem, and, therefore, belong to the class of Lagrangian cuts. To efficiently generate these cuts, we present an enhancement strategy to reduce time-consuming exact evaluations of i…

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.

Tumbling elimination induced by permeability: an experimental approach
Jes\'us S\'anchez-Rodr\'iguez, Fran\c{c}ois Gallaire
https://arxiv.org/abs/2406.01785

Tumbling elimination induced by permeability: an experimental approach
Archetypal falling behaviors of impervious objects are classified into four modes: fluttering, tumbling, steady descent and chaotic motion. The classical scenario predicts these behaviors to be affected by two dimensionless quantities: dimensionless inertia and Reynolds number. In this article we explore experimentally the effect of permeability and porosity on the falling regimes of porous plates. By drilling several hole distributions in rectangular plates, both permeability and porosity are …

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…

The largest subgraph without a forbidden induced subgraph
Jacob Fox, Rajko Nenadov, Huy Tuan Pham
https://arxiv.org/abs/2405.05902 https://

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…

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…

The spiders $S(4m 2,\,2m,\,1)$ are $e$-positivite
Davion Q. B. Tang, David G. L. Wang, Monica M. Y. Wang
https://arxiv.org/abs/2405.04915 https://

The spiders $S(4m+2,\,2m,\,1)$ are $e$-positivite
We establish the $e$-positivity of spider graphs of the form $S(4m+2,\, 2m,\, 1)$, which was conjectured by Aliniaeifard, Wang and van Willigenburg. A key to our proof is the $e_I$-expansion formula of the chromatic symmetric function of paths due to Shareshian and Wachs, where the symbol~$I$ indicates integer compositions rather than partitions. Following the strategy of the divide-and-conquer technique, we pick out one or two positive $e_J$-terms for each negative $e_I$-term in an $e$-express…

This https://arxiv.org/abs/2405.19066 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Note on the Subcubes of the $n$-Cube
In the year 1976, Sergiu Hart considered and solved the following combinatorial problem: given two parameters $k$ and $n$, find a set of k vertices in the $n$-cube which has a maximal number of interconnecting edges. Here we consider the more general problem with $q$-dimensional induced subcubes (for some fixed but arbitrary choice of $q$) instead of the interconnecting edges. In a different, but provably equivalent formulation, this problem has been solved quite recently but the proof that had…

This https://arxiv.org/abs/2202.04794 has been replaced.
link: https://scholar.google.com/scholar?q=a

Non-very generic arrangements in low dimension
The discriminantal arrangement $\mathcal{B}(n,k,\mathcal{A})$ has been introduced by Manin and Schectman in 1989 and it consists of all non-generic translates of a generic arrangement $\mathcal{A}$ of n hyperplanes in a $k$-dimensional space. It is known that its combinatorics depends on the original arrangement A which, following Bayer and Brandt [3], is called very generic if the intersection lattice of the induced discriminantal arrangement has maximum cardinality, non-very generic otherwise…