Related papers: Counting friezes in type D_n
In this paper we apply a geometric covering method to study the number of ends on shrinkers. On one hand, we prove that the number of ends on any complete non-compact shrinker is at most polynomial growth with fixed degree. On the other…
Frieze patterns have an interesting combinatorial structure, which has proven very useful in the study of cluster algebras. We introduce $(k,n)$-frieze patterns, a natural generalisation of the classical notion. A generalisation of the…
We give an elementary account of the notion of Y-frieze patterns, explain some of their properties, and reveal their connection with Coxeter's frieze patterns.
We construct a new presentation of the twisted Yangian of type $D$ with a finite number of generators. By using this presentation, we propose a new definition of the twisted affine Yangian of type $D$.
Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…
For a cluster algebra $\mathcal{A}$ over $\mathbb{Q}$ of geometric type, a $\textit{frieze}$ of $\mathcal{A}$ is defined to be a $\mathbb{Q}$-algebra homomorphism from $\mathcal{A}$ to $\mathbb{Q}$ that takes positive integer values on all…
It is known that any infinite frieze comes from a triangulation of an annulus by Baur, Parsons and Tschabold. In this paper we show that each periodic infinite frieze determines a triangulation of an annulus in essentially a unique way.…
We provide infinitely many solutions of a Dirichlet problem on balls.
Let $n$ be a positive integer, and let $R$ be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether $R$ has at most finitely…
We prove that $d_k(n)=d_k(n+B)$ infinitely often for any positive integers $k$ and $B$, where $d_k(n)$ denotes the number of divisors of $n$ coprime to $k$.
We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d…
We extend a recent result of McKenzie, and show that it is an undecidable problem to determine if 4 appears in the typeset of a finitely generated, locally finite variety.
Consider a simple complex Lie group $G$ acting diagonally on a triple flag variety $G/P_1\times G/P_2\times G/P_3$, where $P_i$ is parabolic subgroup of $G$. We provide an algorithm for systematically checking when this action has finitely…
We construct K(\pi, 1)'s for Artin groups of type C_n and D_n.
We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…
These notes provide three contributions to the (well-established) representation theory of Dynkin and Euclidean quivers. They should be helpful as part of a direct approach to study representations of quivers, and they may shed some new…
We argue that it makes sense to talk about ``typical'' properties of lattices, and then show that there is, up to isomorphism, a unique countable lattice L* (the Fraisse limit of the class of finite lattices) that has all ``typical''…
We analyse the growth coefficients of infinite frieze patterns arising from cluster algebras using cluster modular groups and cluster categories. For a fixed cluster category of affine type, we prove that the collection of infinite frieze…
We construct uncountably many infinite characters of type II for $SL_n(\mathbb{Z})$, $n \geq 2$.
We study the variance of the random variable that counts the number of lattice points in some shells generated by a special class of finite type domains in $\mathbb R^d$. The proof relies on estimates of the Fourier transform of indicator…