Related papers: A naturally appearing family of Cantorvals
This note defines a family of Laurent polynomials (indexed in the rational projective line) which generalize the Markoff numbers and relate to the character variety of the one-cusped torus. We describe which monomials appear in each…
This article is a short and elementary introduction to the monstrous moonshine aiming to be as accessible as possible. I first review the classification of finite simple groups out of which the monster naturally arises, and features of the…
The purpose of this note is to give a survey on recent progress on characteristic classes of flat bundles, and how they behave in a family.
We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.
The aim of the paper is to construct some Godbillon-Vey classes of a family of regular foliations, defined in the paper. These classes are cohomology classes on the manifold or on suitable open subsets. Some examples are also considered.
It is shown that a natural notion of congruence permutability for quasivarieties already implies ``being a variety''. The result follows immediately from [3] and the sole aim of this note is to state it explicitly, together with a…
Our aim is to describe the theory of Cartesian decompositions preserved by some member of a large family of finite transitive permutation groups called innatelytransitive groups.
We introduce a framework for ordinal notation systems, present a family of strong yet simple systems, and give many examples of ordinals in these systems. While much of the material is conjectural, we include systems with conjectured…
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
We solve the long-standing existence problem of vertex-primitive 2-arc-transitive digraphs by constructing an infinite family of such digraphs.
The goal of this note is to give a characterization of generalized quaternion $2$-groups by using their posets of cyclic subgroups.
The goal of this paper is to define families of toric varieties and to study their properties. These families are locally trivial fibrations over some base, whose fibres are isomorphic to a fixed complete toric variety. The study is…
This note is designed to show some classes of differential-difference equations admitting Lax representation which generalize evolutionary equations known in the literature.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the…
These informal notes briefly discuss various aspects of Cantor sets.
We construct a geometrically self-similar Cantor set $X$ of genus $2$ in $\mathbb{R}^3$. This construction is the first for which the local genus is shown to be $2$ at every point of $X$. As an application, we construct, also for the first…
We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it. Assuming such a structure we show that the semantics of various natural language…
The aim of this paper is to realise the techniques of picture-valued invariants and invariants valued in free groups for long knots in the full torus. Such knots and links are of a particular interest because of their relation to Legendrian…