Tootfinder

Enrich your ggplots with extra panels along the x and y axis: #ggplot #dataviz <…

GitHub - jtlandis/ggside: ggplot2 extension allowing for plotting various geometries as side panels using the ggplot2 API
ggplot2 extension allowing for plotting various geometries as side panels using the ggplot2 API - jtlandis/ggside

I think the word that David Frum should lead with the first 2 minutes in https://youtu.be/6zzK5K1ig-Y?si=2-J2Qlimh23VfPHS , " Facts vs. Clicks: How Algorithms Reward Extremism | The David Frum Show x Galaxy Brain " is fascism or dictatorship. Why doesn't he do this? Domin…

On Zero-Dimensional Glicci Monomial Ideals
Benjamin Mudrak
https://arxiv.org/abs/2602.03703 https://arxiv.org/pdf/2602.03703 https://arxiv.org/html/2602.03703
arXiv:2602.03703v1 Announce Type: new
Abstract: Consider the polynomial ring $R_n = k[x_1,...,x_n]$, where $k$ is a field. Let $m = (x_1,...,x_n)$ and $I$ be an $m$-primary monomial ideal in $R$. We consider the problem of determining whether such ideals are in the Gorenstein liasion class of a complete intersection (glicci). We prove that all $m$-primary monomial ideals in $k[x,y,z]$ with at most eight generators are homogeneously glicci. We also construct a large class of $m$-primary monomial ideals in $R_n$ for any $n$ with any number of minimal generators that are homogeneously glicci but not in the complete intersection liaison class of a complete intersection (licci). All Gorenstein links used are constructed explicitly and every second step links to another $m$-primary monomial ideal.
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Unsplittable Transshipments
Srinwanti Debgupta, Sarah Morell, Martin Skutella
https://arxiv.org/abs/2602.07230 https://arxiv.org/pdf/2602.07230 https://arxiv.org/html/2602.07230
arXiv:2602.07230v1 Announce Type: new
Abstract: We introduce the Unsplittable Transshipment Problem in directed graphs with multiple sources and sinks. An unsplittable transshipment routes given supplies and demands using at most one path for each source-sink pair. Although they are a natural generalization of single source unsplittable flows, unsplittable transshipments raise interesting new challenges and require novel algorithmic techniques. As our main contribution, we give a nontrivial generalization of a seminal result of Dinitz, Garg, and Goemans (1999) by showing how to efficiently turn a given transshipment $x$ into an unsplittable transshipment $y$ with $y_a<x_a d_{\max}$ for all arcs $a$, where $d_{\max}$ is the maximum demand (or supply) value. Further results include bounds on the number of rounds required to satisfy all demands, where each round consists of an unsplittable transshipment that routes a subset of the demands while respecting arc capacity constraints.
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Find the best contrast between one color and a list of options, e.g. for labels in geom_tile: {prismatic::best_contrast()} https://emilhvitfeldt.github.io/prismatic/reference/best_contrast.html

Normality of monomial ideals in three variables
Maki Ataka, Naoyuki Matsuoka
https://arxiv.org/abs/2602.01782 https://arxiv.org/pdf/2602.01782 https://arxiv.org/html/2602.01782
arXiv:2602.01782v1 Announce Type: new
Abstract: An ideal $I$ in a Noetherian ring is called \textit{normal} if $I^n$ is integrally closed for all $n \geq 1$. Zariski proved that in two-dimensional regular local rings, every integrally closed ideal is normal. However, in dimension three and higher, this is no longer true in general, including monomial ideals in polynomial rings.
In this paper, we study the normality of integrally closed monomial ideals in the polynomial ring $k[x,y,z]$ over a field $k$. We prove that every such ideal with at most seven minimal monomial generators is normal, thereby giving a sharp bound for normality in this setting. The proof is based on a detailed case-by-case analysis, combined with valuation-theoretic and combinatorial methods via Newton polyhedra.
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