Related papers: A note on friezes of type $\Lambda_p$
Based on Berenstein and Retakh's notion of noncommutative polygons we introduce and study noncommutative frieze patterns. We generalize several notions and fundamental properties from the classic (commutative) frieze patterns to…
We give a geometrically motivated measure of skewness, define a mean value triangle number, and dispersion (in that order) of a fuzzy number without reference or seeking analogy to the namesake but parallel concepts in probability theory.…
In this paper, we introduce and analyze arbitrarily high-order quadrature rules for evaluating the two-dimensional singular integrals of the forms \begin{align} I_{i,j} = \int_{\mathbb{R}^2}\phi(x)\frac{x_ix_j}{|x|^{2+\alpha}} \d x, \quad…
We construct rings of typed ordered fuzzy numbers whose component functions are of a common form. As this ring also contains improper fuzzy numbers (OFNs whose membership "functions" are actually just relations), we develop a set of…
We define "sliding functors", which are exact endofunctors of the category of multi-graded modules over a polynomial ring. They preserve several invariants of modules, especially the (usual) depth and Stanley depth. In a similar way, we can…
A doodle is a collection of immersed circles without triple intersections in the $2$-sphere. It was shown by the second author and P.~Tayler that doodles induce commutator identities (identities amongst commutators) in a free group. In this…
Let $p\geq 5$ be a prime number. We generalize the results of E. de Shalit about supersingular $j$-invariants in characteristic $p$. We consider supersingular elliptic curves with a basis of $2$-torsion over $\overline{\mathbf{F}}_p$, or…
The $\mathcal{B}_p$-algebras are a family of vertex operator algebras parameterized by $p\in \mathbb Z_{\geq 2}$. They are important examples of logarithmic CFTs and appear as chiral algebras of type $(A_1, A_{2p-3})$ Argyres-Douglas…
We introduce a quantisation of the Coxeter-Conway frieze patterns and prove that they realise quantum cluster variables in quantum cluster algebras associated with linearly oriented Dynkin quivers of type A. As an application, we obtain the…
In this article we count tame $ SL_3 $- and $ SL_4 $-frieze patterns with width $ w $ over a finite field $ K $, as well as some tame $ SL_k $-frieze patterns for higher $ k $. Let $ n = w + k + 1 $. We consider the sets $ C_k(n) $ of…
We establish some identities of Euler related sums. By using these identities, we discuss the closed form representations of sums of harmonic numbers and reciprocal parametric binomial coefficients through parametric harmonic numbers,…
All edge-to-edge tilings of the sphere by congruent regular triangles and congruent rhombi are classified as: (1) a $1$-parameter family of protosets each admitting a unique $(2a^3,3a^4)$-tiling like a triangular prism; (2) a $1$-parameter…
Each acyclic graph, and more generally, each acyclic orientation of the graph associated to a Cartan matrix, allows to define a so-called frise; this is a collection of sequences over the positive natural numbers, one for each vertex of the…
Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…
We study syzygies of the Segre embedding of P(V_1) x ... x P(V_n), and prove two finiteness results. First, for fixed p but varying n and V_i, there is a finite list of "master p-syzygies" from which all other p-syzygies can be derived by…
An embedded graph is called $z$-knotted if it contains the unique zigzag (up to reversing). We consider $z$-knotted triangulations, i.e. $z$-knotted embedded graphs whose faces are triangles, and describe all cases when the connected sum of…
A leaper framework is a bar-and-joint framework whose joints are integer points forming a rectangular grid and whose bars correspond to all moves of a given leaper within that grid. We study the flexibility and rigidity of leaper…
Let $f: \mathbb{Z}_+\rightarrow \mathbb{Z}_+$ be a polynomial with the property that corresponding to every prime $p$ there exists an integer $\ell$ such that $p\nmid f(\ell)$. In this paper, we establish some equidistributed results…
ML is remarkable in providing statically typed polymorphism without the programmer ever having to write any type annotations. The cost of this parsimony is that the programmer is limited to a form of polymorphism in which quantifiers can…
Given a real function $f$ on an interval $[a,b]$ satisfying mild regularity conditions, we determine the number of zeros of $f$ by evaluating a certain integral. The integrand depends on $f, f'$ and $f''$. In particular, by approximating…