Tootfinder

General symmetric ideals
Alexandra Seceleanu, Liana \c{S}ega
https://arxiv.org/abs/2506.15459 https://arxiv.org/pdf/2506.15459…

General symmetric ideals
We investigate the structure and properties of symmetric ideals generated by general forms in the polynomial ring under the natural action of the symmetric group. This work significantly broadens the framework established in our earlier collaboration with Harada on principal symmetric ideals. A novel aspect of our approach is the construction of a bijective parametrization of general symmetric ideals using Macaulay-Matlis duality, which is asymptotically independent of the number of variables o…

Algorithmic resolution of crowd-sourced moderation on X in polarized settings across countries
Paul Bouchaud, Pedro Ramaciotti
https://arxiv.org/abs/2506.15168

Algorithmic resolution of crowd-sourced moderation on X in polarized settings across countries
Social platforms increasingly transition from expert fact-checking to crowd-sourced moderation, with X pioneering this shift through its Community Notes system, enabling users to collaboratively moderate misleading content. To resolve conflicting moderation, Community Notes learns a latent ideological dimension and selects notes garnering cross-partisan support. As this system, designed for and evaluated in the United States, is now deployed worldwide, we evaluate its operation across diverse p…

“We got to be honest in what happened, because losing elections has consequences,”
said Minnesota Gov. Tim Walz, Harris’ running mate,
during a rousing speech Saturday afternoon.
“We’re in this mess because some of it’s our own doing. … None of us can afford to shy away from having hard conversations about what it’s going to take to win elections.”
Walz, a potential 2028 presidential candidate, said Democrats don’t need to retreat from their ideals,
such as pro…

Democrats vow to stick to values while regaining working-class voters
California Democrats say their party must stay committed to their values protecting the most vulnerable, while also honing their economic messaging to win back voters they lost last year.

This https://arxiv.org/abs/2503.16393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiplicity $=$ Volume formula and Newton non-degenerate ideals in regular local rings
We develop the notions of Newton non-degenerate (NND) ideals and Newton polyhedra for regular local rings. These concepts were first defined in the context of complex analysis. We show that the characterization of NND ideals via their integral closures known in the analytical setting extends to regular local rings. We use the limiting body $\mathcal{C}(\mathcal{I})$ associated to a graded family $\mathcal{I}$ of ideals to provide a new understanding of the celebrated "Multiplicity $=$ Volume" f…

This https://arxiv.org/abs/2503.16393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiplicity $=$ Volume formula and Newton non-degenerate ideals in regular local rings
We develop the notions of Newton non-degenerate (NND) ideals and Newton polyhedra for regular local rings. These concepts were first defined in the context of complex analysis. We show that the characterization of NND ideals via their integral closures known in the analytical setting extends to regular local rings. We use the limiting body $\mathcal{C}(\mathcal{I})$ associated to a graded family $\mathcal{I}$ of ideals to provide a new understanding of the celebrated "Multiplicity $=$ Volume" f…

An Early History of Toric Ideals
Serkan Ho\c{s}ten
https://arxiv.org/abs/2505.18443 https://arxiv.org/pdf/2505.18443

An Early History of Toric Ideals
Toric ideals are everywhere. They have been in the commutative algebra lexicon since about 1990 when Bernd Sturmfels used the term. The early days of toric ideals and their Gröbner bases were full of new results and promising developments in their applications. Bernd has been consistently their biggest promoter through his own work and that of his collaborators and students. This article is a personal and subjective recalling of the first decade of toric ideals when Bernd played a central role.

An Early History of Toric Ideals
Serkan Ho\c{s}ten
https://arxiv.org/abs/2505.18443 https://arxiv.org/pdf/2505.18443

An Early History of Toric Ideals
Toric ideals are everywhere. They have been in the commutative algebra lexicon since about 1990 when Bernd Sturmfels used the term. The early days of toric ideals and their Gröbner bases were full of new results and promising developments in their applications. Bernd has been consistently their biggest promoter through his own work and that of his collaborators and students. This article is a personal and subjective recalling of the first decade of toric ideals when Bernd played a central role.

Ordinary and symbolic powers of matroids via polarization
Justin Lyle, Paolo Mantero
https://arxiv.org/abs/2505.17398 https://arxiv.o…

Ordinary and symbolic powers of matroids via polarization
In this paper, we propose a uniform approach to tackle problems about squarefree monomial ideals whose powers have good properties. We employ this approach to achieve a twofold goal: (i) recover and extend several well--known results in the literature, especially regarding Stanley--Reisner ideals of matroids, and (ii) provide short, elementary proofs for these results. Among them, we provide simple proofs of two celebrated results of Minh and Trung, Varbaro, and Terai and Trung elegantly charac…

Ordinary and symbolic powers of matroids via polarization
Justin Lyle, Paolo Mantero
https://arxiv.org/abs/2505.17398 https://arxiv.o…

Ordinary and symbolic powers of matroids via polarization
In this paper, we propose a uniform approach to tackle problems about squarefree monomial ideals whose powers have good properties. We employ this approach to achieve a twofold goal: (i) recover and extend several well--known results in the literature, especially regarding Stanley--Reisner ideals of matroids, and (ii) provide short, elementary proofs for these results. Among them, we provide simple proofs of two celebrated results of Minh and Trung, Varbaro, and Terai and Trung elegantly charac…