Tootfinder

Structural results on idealistic equivalence relations
Filippo Calderoni, Luca Motto Ros
https://arxiv.org/abs/2506.08217 https://arx…

Structural results on idealistic equivalence relations
We address some fundamental problems concerning the structure of idealistic equivalence relations. In particular, we show that, under analytic determinacy, there are continuum many idealistic analytic equivalence relations that are not classwise Borel isomorphic to an orbit equivalence relation. Moreover, we also discuss alternative formulations of the E1 conjecture, and present an elementary counterexample to one of its earliest variants proposed by Hjorth and Kechris in 1997.

Errol Musk, the father of U.S. billionaire Elon Musk,
has arrived in Moscow to attend the Forum of the Future 2050,
a pro-Kremlin event scheduled for June 9-10,  the Russian newspaper Kommersant reported on June 8.
https://kyivindepend…

Elon Musk's father to attend pro-Kremlin event in Russia hosted by far-right ideologue
Among the forum's panels are sessions titled "Russian Space: The Race for Mars" and "The Battle for Hearts and Minds: The Ideology of Sovereign Russia."

This https://arxiv.org/abs/2312.01613 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Binomial Edge Ideals of Complements of Graphs of Girth at Least 5
We calculate the local cohomology modules of the binomial edge ideals of the complements of graphs of girth at least 5 using the tools introduced by Àlvarez Montaner in arXiv:1901.08645. We then use this calculation to compute the depth, dimension, and regularity of these binomial edge ideals.

On ideals of product of commutative rings and their applications
Mehdi Badie, Ali Rezaie Aliabad, Foad Obeidavi
https://arxiv.org/abs/2506.08537 https://…

On ideals of product of commutative rings and their applications
In this paper, leveraging the recent achievements of researchers, we have revisited the family of ideals of product of commutative rings. We demonstrate that if $ \{ R_α\}_{α\in A} $ is an infinite family of rings, then $ \left| Max \left( \prod_{α\in A} R_α\right) \right| \geqslant 2^{2^{|A|}} $. Notably, if these rings are local then the equality holds. We establish that $ Max(R_α) $ is homeomorphic to a closed subset of $ Max \left( \prod_{α\in A} R_α\right) $, for…

Intressant i "Älskade politik" om hur regeringskansliet numera försöker stoppa "paper trails" i många fall – och de "ideologiska skälen" till stoppet för Unrwa-stödet. https://www.dn.se/podd/alskade-politik/tomtar-och-t…

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Jag reflekterar över varför jag gör det jag gör och hur jag vill nyttja min tid. Mitt skrivande är mitt kall, och tillsammans med mina modeller och visualiseringar är det så just jag kan bidra. Nu kan du som vill och har förmåga också backa det arbetet.

"År 1973 skrev Ursula K. Le Guin sin prisbelönta berättelse De som går bort från Omelas. Denna korta science fiction-berättelse beskriver en idyllisk stad, Omelas, där alla mä…

Here's my latest Boles Bells article!
https://bolesbells.com/blog/2025/6/9/the-iron-ballast-kettlebells-national-identity-and-the-russian-mythos-of-strength

The Iron Ballast: Kettlebells, National Identity, and the Russian Mythos of Strength — David Boles Bells
The trajectory of Russia over the past century is a story deeply etched with societal upheavals, ideological fervor, and an unyielding quest for national assertion on the global stage. Knotted into this complex tapestry is the seemingly modest history of the kettlebell, or girya . This unassuming i

🇺🇦 #NowPlaying on KEXP's #MorningShow
IDLES:
🎵 Colossus
#IDLES
https://idlesband.bandcamp.com/track/colossus
https://open.spotify.com/track/4wf2tcIlvAxVBsjykZha71

This https://arxiv.org/abs/2505.04248 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On minimal free resolutions of the cover ideals of clique-whiskered graphs
We explicitly construct a minimal free resolution of the cover ideals of clique-whiskered graphs. In particular, Cohen--Macaulay chordal graphs, clique corona graphs, and Cohen--Macaulay Cameron--Walker graphs are examples of clique-whiskered graphs. We also introduce multi-clique-whiskered graphs as a generalization of both clique-whiskered graphs and multi-whisker graphs. We prove that multi-clique-whiskered graphs are vertex decomposable and hence sequentially Cohen--Macaulay. Moreover, we p…

This https://arxiv.org/abs/2410.20188 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Bernstein-Sato functional equations for ideals in positive characteristic
For an ideal of a regular $\cc$-algebra, its Bernstein-Sato polynomial is the monic polynomial of the lowest degree satisfying an Bernstein-Sato functional equation. We generalize the notion of Bernstein-Sato functional equations to the case of ideals in an $F$-finite ring of positive characteristic $p$, and show the relationship between these equations and Bernstein-Sato roots. By applying this theory, we provide an explicit description of Bernstein-Sato roots of a weighted homogeneous polynom…