Related papers: Homogeneous 3-dimensional permutation structures
We show that several classes of ordered structures (namely, convex linear orders, layered permutations, and compositions) admit first-order logical limit laws.
We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit…
We describe and compute the homotopy of spectra of topological modular forms of level 3. We give some computations related to the "building complex" associated to level 3 structures at the prime 2. Finally, we note the existence of a number…
We give a complete characterization of invariant integrable complex structures on principal bundles defined over hermitian symmetric spaces, using the Jordan algebraic approach for the curvature computations. In view of possible…
A relational structure $\mathbb{X}$ is called reversible iff each bijective homomorphism from $\mathbb{X}$ onto $\mathbb{X}$ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible…
We provide a complete classification of hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions: 1) the Chern connection remains holomorphic at the singular point, 2) the web admits at least one…
Recent work has proven that training large language models with self-supervised tasks and fine-tuning these models to complete new tasks in a transfer learning setting is a powerful idea, enabling the creation of models with many…
The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
We classify the 5-dimensional homogeneous geometries in the sense of Thurston. The present paper (part 3 of 3) classifies those in which the linear isotropy representation is nontrivial but reducible. Most of the resulting geometries are…
We determine the homological dimension of various isogeny categories of commutative algebraic groups over a field $k$, in terms of the cohomological dimension of $k$ at certain primes. This generalizes results of Serre, Oort and Milne, by…
We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…
This paper studies 3-polygraphs as a framework for rewriting on two-dimensional words. A translation of term rewriting systems into 3-polygraphs with explicit resource management is given, and the respective computational properties of each…
In this paper we investigate the simplicial structure of a chain complex associated to the higher order Hochschild homology over the $3$-sphere. We also introduce the tertiary Hochschild homology corresponding to a quintuple…
We discuss hidden symmetries of three-dimensional field configurations revealed at the one-particle level by the use of pseudoclassical particle models. We argue that at the quantum field theory level, these can be naturally explained in…
The underlying structure of natural language is hierarchical; words combine into phrases, which in turn form clauses. An awareness of this hierarchical structure can aid machine learning models in performing many linguistic tasks. However,…
One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…
We consider various $A_{\infty}$-algebras of differential (super)forms, which are related to gauge theories and demonstrate explicitly how certain reformulations of gauge theories lead to the transfer of the corresponding…
An infinite permutation is a linear order on the set N. We study the properties of infinite permutations generated by fixed points of some uniform binary morphisms, and find the formula for their complexity.
We consider mixed normed Bergman spaces on homogeneous Siegel domains. In the literature, two different approaches have been considered and several results seem difficult to be compared. In this paper we compare the results available in the…