Related papers: Spider's webs of doughnuts

We mainly generalize the notion of abelian transcendental semigroup to nearly abelian transcendental semigroup. We prove that Fatou set, Julia set and escaping set of nearly abelian transcendental semigroup are completely invariant. We…

Given a polynomial diffeomorphism f: C^2 -> C^2 there is a set $J_f\subset{\bf C}^2$ which we call the Julia set of f. The set $J_f\subset C^2$ plays the role of the Julia set $J\subset{\bf C}$ for a polynomial map of C. In the study of…

In the affine space $\mathbb{F}_q^n$ over the finite field of order $q$, a point set $S$ is said to be $(d,k,r)$-evasive if the intersection between $S$ and any variety, of dimension $k$ and degree at most $d$, has cardinality less than…

Webs are combinatorial diagrams used to encode homomorphisms between representations of Lie (super)algebras and related objects. This paper extends the theory of webs to the quantum group of type Q. We define a monoidal supercategory of…

Let $\mathcal{F}$ be any collection of linearly separable sets of a set $P$ of $n$ points either in $\mathbb{R}^2$, or in $\mathbb{R}^3$. We show that for every natural number $k$ either one can find $k$ pairwise disjoint sets in…

We show that if the growth of a transcendental entire function f is sufficiently regular, then the Julia set and the escaping set of f have Hausdorff dimension 2.

We define a suffixient set for a text $T [1..n]$ to be a set $S$ of positions between 1 and $n$ such that, for any edge descending from a node $u$ to a node $v$ in the suffix tree of $T$, there is an element $s \in S$ such that $u$'s path…

Barnette's conjecture is an unsolved problem in graph theory. The problem states that every 3-regular (cubic), 3-connected, planar, bipartite (Barnette) graph is Hamiltonian. Partial results have been derived with restrictions on number of…

We consider the iteration of quasiregular maps of transcendental type from $\mathbb{R}^d$ to $\mathbb{R}^d$. We give a bound on the rate at which the iterates of such a map can escape to infinity in a periodic component of the quasi-Fatou…

According to the Thurston No Wandering Triangle Theorem, a branching point in a locally connected quadratic Julia set is either preperiodic or precritical. Blokh and Oversteegen proved that this theorem does not hold for higher degree Julia…

Given a point set $P$ in the Euclidean space, a geometric $t$-spanner $G$ is a graph on $P$ such that for every pair of points, the shortest path in $G$ between those points is at most a factor $t$ longer than the Euclidean distance between…

Consider a simple algebraic group $G$ of classical type and its Lie algebra $\mathfrak{g}$. Let $(e,h,f) \subset \mathfrak{g}$ be an $\mathfrak{sl}_2$-triple and $Q_e= C_G(e,h,f)$. The torus $T_e$ that comes from the…

Let $L$ be a prime alternating link with $n$ crossings. We show that for each fixed $g$, the number of genus $g$ incompressible surfaces in the complement of $L$ is bounded by a polynomial in $n$. Previous bounds were exponential in $n$.

It is well-known that the Julia set J(f) of a rational map is uniformly perfect; that is, every ring domain which separates J(f) has bounded modulus, with the bound depending only on f. In this article we prove that an analogous result is…

Let R be a two-dimensional regular local ring having an algebraically closed residue field and let a be a complete ideal of finite colength in R. In this article we investigate the jumping numbers of a by means of the dual graph of the…

Pattern-avoiding permutations are a central object of study in both combinatorics and theoretical computer science. In this paper we design a data structure that can store any size-$n$ permutation $\tau$ that avoids an arbitrary (and…

Consider $d$ disjoint closed subintervals of the unit interval and consider an orientation preserving expanding map which maps each of these subintervals to the whole unit interval. The set of points where all iterates of this expanding map…

A Peano compactum is a compact metric space having locally connected components such that at most finitely many of them are of diameter greater than any fixed number C>0. Given a compactum K in the extended complex plane, it is known that…

We design sensitivity oracles for error-prone networks. For a network problem $\Pi$, the data structure preprocesses a network $G=(V,E)$ and sensitivity parameter $f$ such that, for any set $F\subseteq V\cup E$ of up to $f$ link or node…

For G a semisimple algebraic group, we revisit the description of the components of the affne Springer fiber given by ts, with s a regular semisimple element. We then compute the fixed points of each component of a particular affne Springer…