Tootfinder

This https://arxiv.org/abs/2504.21059 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A remark on the number of automorphisms of some algebraic structures
In these notes we look at the following question. Given a category $\mathcal C$ of algebraic structure (e.g. the category of groups, monoids, partial groups, ...) and a rational $r\in \mathbb Q$, does there exists an element $x\in \mathcal C$ such that the size of its automorphism group $\text{Aut}_{\mathcal C} (x)$ divided by the size of $x$ (whatever that would means) is equal to $r$\,? To our knowledge, this question was introduced by Tărnăuceanu in the category of groups. Here, we answer …

A Real K3 Automorphism with Most of Its Entropy in the Real Part
Ethan Cohen
https://arxiv.org/abs/2506.03479 https://arxiv.org/pdf/2…

A Real K3 Automorphism with Most of Its Entropy in the Real Part
This article describes an example of a real projective K3 surface admitting a real automorphism $f$ satisfying $h_{top}(f, X(\mathbb{C})) < 2 h_{top}(f, X(\mathbb{R}))$. The example presented is a $(2,2,2)$-surface in $\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1$ given by the vanishing set of $(1 + x^2)(1 + y^2)(1 + z^2) + 10xyz - 2$, first considered by McMullen. Along the way, we develop an ad hoc shadowing lemma for $C^2$ (real) surface diffeomorphisms, and apply it to estimate the …

Improving AI-generated music with user-guided training
Vishwa Mohan Singh, Sai Anirudh Aryasomayajula, Ahan Chatterjee, Beste Aydemir, Rifat Mehreen Amin
https://arxiv.org/abs/2506.04852

Improving AI-generated music with user-guided training
AI music generation has advanced rapidly, with models like diffusion and autoregressive algorithms enabling high-fidelity outputs. These tools can alter styles, mix instruments, or isolate them. Since sound can be visualized as spectrograms, image-generation algorithms can be applied to generate novel music. However, these algorithms are typically trained on fixed datasets, which makes it challenging for them to interpret and respond to user input accurately. This is especially problematic beca…

This https://arxiv.org/abs/2407.09997 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The most symmetric smooth cubic surface
In this paper for any field of characteristic different from 2 we find the largest automorphism group of a smooth cubic surface over this field. Moreover, we prove that for a given field a smooth cubic surface with the largest automorphism group is unique up to isomorphism.

Ugghhhhh https://urbanists.social/@enobacon/114628927949380555

#WritersCoffeeClub 5: Talk about something you’ve read that made you think, 'I wish I wrote that.'
Most anything of Sir Terry Pratchett, I have an immense admiration for his wit, his humour, his intelligence, and his writing. I'm not remotely funny, not in my opinion anyway, which makes me awestruck when I find someone who is.

Graph quandles: Generalized Cayley graphs of racks and right quasigroups
Luc Ta
https://arxiv.org/abs/2506.04437 https://arxiv.org/pd…

Graph quandles: Generalized Cayley graphs of racks and right quasigroups
We solve two open problems of Valeriy Bardakov about Cayley graphs of racks and graph-theoretic realizations of right quasigroups. We also extend Didier Caucal's classification of labeled Cayley digraphs to right quasigroups and related algebraic structures like quandles. First, we characterize markings of graphs that realize racks. As an application, we construct rack-theoretic (di)graph invariants from permutation representations of graph automorphism groups. We describe how to compute thes…

🇺🇦 Auf radioeins läuft...
Roisín Murphy:
🎵 Murphy's Law
#NowPlaying #RoisínMurphy
https://simondunmore.bandcamp.com/track/murphys-law-extended-mix
https://open.spotify.com/track/5pVk9zx3qrtmx3ya8hyanZ

This https://arxiv.org/abs/2208.00676 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Pansiot-type subword complexity theorem for automorphisms of free groups
Inspired by Pansiot's work on substitutions, we prove a similar theorem for automorphisms of a free group F of finite rank: if a right-infinite word X represents an attracting fixed point of an automorphism of F, the subword complexity of X is equivalent to n, n log log n, n log n, or n^2. The proof uses combinatorial arguments analogue to Pansiot's as well as train tracks. We also define the recurrence complexity of X, and we apply it to laminations. In particular, we show that attracting lami…

The McCullough-Miller complex for right angled Artin groups
Peio Ardaiz Gal\'e, Conchita Mart\'inez P\'erez
https://arxiv.org/abs/2506.03377 ht…

The McCullough-Miller complex for right angled Artin groups
McCullough and Miller constructed a contractible complex on which the pure symmetric automorphism group of a free group acts with free abelian stabilizers. This complex has been used for computations such as the cohomological dimension of these groups, their cohomology rings, and results about $\ell^2$-Betti numbers or BNRS-invariants. We generalize this construction to pure symmetric automorphism groups of arbitrary RAAGs and exhibit applications of this generalization.