Related papers: Counting siblings in universal theories

We present a conjecture on multiplicity of irreducible representations of a subgroup $H$ contained in the irreducible representations of a group $G$, with $G$ and $H$ having the same derived groups. We point out some consequences of the…

We prove that the problems of representing a finite ordered complemented semigroup or finite lattice-ordered semigroup as an algebra of binary relations over a finite set are undecidable. In the case that complementation is taken with…

We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but…

Let $M$ be a Fra\"{i}ss\'{e} structure (a countably infinite ultrahomogeneous structure). We refer to the class of structures embeddable in $M$ as the $\omega$-age of $M$. We consider the following two properties of $M$: we say that $M$ has…

A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…

We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…

We show that every countable Borel equivalence relation structurable by $n$-dimensional contractible simplicial complexes embeds into one which is structurable by such complexes with the further property that each vertex belongs to at most…

We construct HNN-extensions of Lie superalgebras and prove that every Lie superalgebra embeds into any of its HNN-extensions. Then as an application we show that any Lie superalgebra with at most countable dimension embeds into a…

Let $k$ be a field containing an algebraically closed field of characteristic zero. If $G$ is a finite group and $D$ is a division algebra over $k$, finite dimensional over its center, we can associate to a faithful $G$-grading on $D$ a…

In the note some construction of Lie algebras is introduced. It is proved that the construction has the same property as a well known wreath product of groups [1]: Any extension of groups can be embedded into their wreath product [2].

We consider the $ r = 0 $ case of the conjectures by Bonnaf\'e, Geck, Iancu and Lam on cellular structures on the Hecke algebra of type $ B $. We show that this case induces the natural cell structure on the blob algebra $ b_n $ by…

We say a structure $M$ in a first-order language is indivisible if for every coloring of its universe in two colors, there is a monochromatic substructure $M'$ of $M$ such that $M'$ is isomorphic to $M$. Additionally, we say that $M$ is…

Working in the framework of Borel reducibility, we study various notions of embeddability between groups. We prove that the embeddability between countable groups, the topological embeddability between (discrete) Polish groups, and the…

We define the continuous modeling property for first-order structures and show that a first-order structure has the continuous modelling property if and only if its age has the embedding Ramsey property. We use generalized indiscernible…

We prove a structural result for sets of integers with doubling at most $4 + \delta$, with $\delta>0$ sufficiently small. This generalises earlier work of Eberhard--Green--Manners which dealt with sets of integers with doubling strictly…

In noncommutative geometry a `Lie algebra' or bidirectional bicovariant differential calculus on a finite group is provided by a choice of an ad-stable generating subset C stable under inversion. We study the associated Killing form. For…

Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…

We give an example of a countable theory T such that for every cardinal lambda >= aleph_2 there is a fully indiscernible set A of power lambda such that the principal types are dense over A, yet there is no atomic model of T over A. In…

We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…

A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…