Search results for "combinatoric"
showing 10 items of 1776 documents
Catalan and Schröder permutations sortable by two restricted stacks
2020
Abstract Pattern avoiding machines were introduced recently by Claesson, Cerbai and Ferrari as a particular case of the two-stacks in series sorting device. They consist of two restricted stacks in series, ruled by a right-greedy procedure and the stacks avoid some specified patterns. Some of the obtained results have been further generalized to Cayley permutations by Cerbai, specialized to particular patterns by Defant and Zheng, or considered in the context of functions over the symmetric group by Berlow. In this work we study pattern avoiding machines where the first stack avoids a pair of patterns of length 3 and investigate those pairs for which sortable permutations are counted by the…
Quasisymmetric extension on the real line
2018
We give a geometric characterization of the sets $E\subset \mathbb{R}$ that satisfy the following property: every quasisymmetric embedding $f: E \to \mathbb{R}^n$ extends to a quasisymmetric embedding $f:\mathbb{R}\to\mathbb{R}^N$ for some $N\geq n$.
A rigidity theorem for the pair ${\cal q}{\Bbb C} P^n$ (complex hyperquadric, complex projective space)
1999
Given a compact Kahler manifold M of real dimension 2n, let P be either a compact complex hypersurface of M or a compact totally real submanifold of dimension n. Let \(\cal q\) (resp. \({\Bbb R} P^n\)) be the complex hyperquadric (resp. the totally geodesic real projective space) in the complex projective space \({\Bbb C} P^n\) of constant holomorphic sectional curvature 4\( \lambda \). We prove that if the Ricci and some (n-1)-Ricci curvatures of M (and, when P is complex, the mean absolute curvature of P) are bounded from below by some special constants and volume (P) / volume (M) \(\leq \) volume (\(\cal q\))/ volume \(({\Bbb C} P^n)\) (resp. \(\leq \) volume \(({\Bbb R} P^n)\) / volume …
Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains
2019
AbstractThe conformal mapping $$f(z)=(z+1)^2 $$ f ( z ) = ( z + 1 ) 2 from $${\mathbb {D}}$$ D onto the standard cardioid has a homeomorphic extension of finite distortion to entire $${\mathbb {R}}^2 .$$ R 2 . We study the optimal regularity of such extensions, in terms of the integrability degree of the distortion and of the derivatives, and these for the inverse. We generalize all outcomes to the case of conformal mappings from $${\mathbb {D}}$$ D onto cardioid-type domains.
Invariant Jordan curves of Sierpinski carpet rational maps
2015
In this paper, we prove that if $R\colon\widehat{\mathbb{C}}\to\widehat{\mathbb{C}}$ is a postcritically finite rational map with Julia set homeomorphic to the Sierpi\'nski carpet, then there is an integer $n_0$, such that, for any $n\ge n_0$, there exists an $R^n$-invariant Jordan curve $\Gamma$ containing the postcritical set of $R$.
Multi-layer canard cycles and translated power functions
2008
Abstract The paper deals with two-dimensional slow-fast systems and more specifically with multi-layer canard cycles. These are canard cycles passing through n layers of fast orbits, with n ⩾ 2 . The canard cycles are subject to n generic breaking mechanisms and we study the limit cycles that can be perturbed from the generic canard cycles of codimension n . We prove that this study can be reduced to the investigation of the fixed points of iterated translated power functions.
Feuilletages deCP(n) : de l’holonomie hyperbolique pour les minimaux exceptionnels
1992
Let ℱ be a holomorphic foliation ofCP(n). If ℱ has a leaf L, the closure L of which is disjoint from the singular set of the foliation, we prove that there exists a loop in a leaf contained in L with contracting hyperbolic holonomy.
Pseudo-rotations of the closed annulus : variation on a theorem of J. Kwapisz
2003
Consider a homeomorphism h of the closed annulus S^1*[0,1], isotopic to the identity, such that the rotation set of h is reduced to a single irrational number alpha (we say that h is an irrational pseudo-rotation). For every positive integer n, we prove that there exists a simple arc gamma joining one of the boundary component of the annulus to the other one, such that gamma is disjoint from its n first iterates under h. As a corollary, we obtain that the rigid rotation of angle alpha can be approximated by homeomorphisms conjugate to h. The first result stated above is an analog of a theorem of J. Kwapisz dealing with diffeomorphisms of the two-torus; we give some new, purely two-dimension…
The variation of the maximal function of a radial function
2017
We study the problem concerning the variation of the Hardy-Littlewood maximal function in higher dimensions. As the main result, we prove that the variation of the non-centered Hardy-Littlewood maximal function of a radial function is comparable to the variation of the function itself.
The Bishop–Phelps–Bollobás point property
2016
Abstract In this article, we study a version of the Bishop–Phelps–Bollobas property. We investigate a pair of Banach spaces ( X , Y ) such that every operator from X into Y is approximated by operators which attain their norm at the same point where the original operator almost attains its norm. In this case, we say that such a pair has the Bishop–Phelps–Bollobas point property (BPBpp). We characterize uniform smoothness in terms of BPBpp and we give some examples of pairs ( X , Y ) which have and fail this property. Some stability results are obtained about l 1 and l ∞ sums of Banach spaces and we also study this property for bilinear mappings.