Related papers: Factorization of Frieze Patterns
We prove a function field analogue of a conjecture of Schinzel on the factorization of univariate polynomials over the rationals. We derive from it a finiteness theorem for the irreducible factorizations of the bivariate Laurent polynomials…
We investigate compressibility of the dimension of positive semidefinite matrices while approximately preserving their pairwise inner products. This can either be regarded as compression of positive semidefinite factorizations of…
The famous theorem of Conway and Coxeter on frieze patterns gave a geometric interpretation to integral friezes via triangulations of polygons. In this article, we review this result and show some of the development it has led to. The last…
We obtain several rigidity results regarding tensor product decompositions of factors. First, we show that any full factor with separable predual has at most countably many tensor product decompositions up to stable unitary conjugacy. We…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…
We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes. Our construction works not…
Every absolutely summing linear operator is weakly compact. However, for strongly summing multilinear operators and polynomials - one of the most natural extensions of the linear case to the non linear framework - weak compactness does not…
For an element $a$ of an integral domain D under an equivalence relation \tau, the \tau-factorization of a is defined as \lambda a_1 a_2... a_k, where \lambda is a unit in D and a_i \tau a_j for all i, j. An irreducible element has no…
We give a new expression for the number of factorizations of a full cycle into an ordered product of permutations of specified cycle types. This is done through purely algebraic means, extending work of Biane. We deduce from our result a…
We undertake a detailed investigation into the structure of permutations in monotone grid classes whose row-column graphs do not contain components with more than one cycle. Central to this investigation is a new decomposition, called the…
All known structural extensions of the substructural logic $\mathsf{FL_e}$, Full Lambek calculus with exchange/commutativity, (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$-equations)…
I suggest that the current situation in quantum field theory (QFT) provides some reason to question the universal validity of ontological reductionism. I argue that the renormalization group flow is reversible except at fixed points, which…
A frieze on a polygon is a map from the diagonals of the polygon to an integral domain which respects the Ptolemy relation. Conway and Coxeter previously studied positive friezes over $\mathbb{Z}$ and showed that they are in bijection with…
In this paper we show that a split central simple algebra with quadratic pair which decomposes into a tensor product of quaternion algebras with involution and a quaternion algebra with quadratic pair is adjoint to a quadratic Pfister form.…
Let W be an arbitrary Coxeter group. If two elements have expressions that are cyclic shifts of each other (as words), then they are conjugate (as group elements) in W. We say that w is "cyclically fully commutative" (CFC) if every cyclic…
The total multiplicity in the decomposition into irreducibles of the tensor product i x j of two irreducible representations of a simple Lie algebra is invariant under conjugation of one of them sum_k N_{i j}^{k}= sum_k N_{ibar j}^{k}. This…
Irreversibility is usually captured by a comparison between the process that happens and a corresponding "reverse process". In the last decades, this comparison has been extensively studied through fluctuation relations. Here we revisit…
$\lambda$-quiddities of size $n$ are $n$-tuples of elements from a fixed set that are solutions to a matrix equation which is fundamental in the study of the combinatorics of the modular group and Coxeter's friezes. To gain further insight…
For the integrable spin-s XXZ chain we express explicitly any given spin-$s$ form factor in terms of a sum over the scalar products of the spin-1/2 operators. Here they are given by the operator-valued matrix elements of the monodromy…
We begin by showing that any $n \times n$ matrix can be decomposed into a sum of $n$ circulant matrices with periodic relaxations on the unit circle. This decomposition is orthogonal with respect to a Frobenius inner product, allowing…