Search results for "Combinatorics"

The Bohr Radius of a Banach Space

2009

Following the scalar-valued case considered by Djakow and Ramanujan (A remark on Bohr’s theorem and its generalizations 14:175–178, 2000) we introduce, for each complex Banach space X and each \(1\le p0\). We study the p-Bohr radius of the Lebesgue spaces \(L^q(\mu )\) for different values of p and q. In particular we show that \(r_p(L^q(\mu ))=0\) whenever \(p<2\) and \(dim(L^q(\mu ))\ge 2\) and \(r_p(L^q(\mu ))=1\) whenever \(p\ge 2\) and \(p'\le q\le p\). We also provide some lower estimates for \(r_2(L^q(\mu ))\) for the values \(1\le q<2\).

Forests and pattern-avoiding permutations modulo pure descents

2018

Abstract We investigate an equivalence relation on permutations based on the pure descent statistic. Generating functions are given for the number of equivalence classes for the set of all permutations, and the sets of permutations avoiding exactly one pattern of length three. As a byproduct, we exhibit a permutation set in one-to-one correspondence with forests of ordered binary trees, which provides a new combinatorial class enumerated by the single-source directed animals on the square lattice. Furthermore, bivariate generating functions for these sets are given according to various statistics.

Quantum Walks on Two-Dimensional Grids with Multiple Marked Locations

2016

The running time of a quantum walk search algorithm depends on both the structure of the search space graph and the configuration of marked locations. While the first dependence has been studied in a number of papers, the second dependence remains mostly unstudied. We study search by quantum walks on the two-dimensional grid using the algorithm of Ambainis, Kempe and Rivosh [AKR05]. The original paper analyses one and two marked locations only. We move beyond two marked locations and study the behaviour of the algorithm for an arbitrary configuration of marked locations. In this paper, we prove two results showing the importance of how the marked locations are arranged. First, we present tw…

Taille critique et stratégie du distributeur - Analyse théorique et implications managériales

1998

International audience; La notion de taille critique a été généralement invoquée par les distributeurs pour justifier les opérations de croissance externe qui demeurent unepratique stratégique importante dans ce secteur. Cet article propose une revue des arguments qui supportent et contredisent l’existence d’une taillecritique pouvant guider les décisions stratégiques des distributeurs, et envisage les implications managériales de la remise en cause de cette notion.

La relation client sur Internet : les banques mettent leurs clients au travail

2009

Le client, sur Internet, est amene a prendre une place de plus en plus importante dans le processus de servuction. A ce titre, il devient coproducteur et remplace meme, dans de nombreux cas, les salaries des entreprises. Le secteur bancaire a largement participe a cette externalisation de certains services vers ses clients. Nous etudierons ce phenomene et ses consequences pour la gestion de la relation client.

Commuting powers and exterior degree of finite groups

2011

In [P. Niroomand, R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335-343] it is introduced a group invariant, related to the number of elements $x$ and $y$ of a finite group $G$, such that $x \wedge y = 1_{G \wedge G}$ in the exterior square $G \wedge G$ of $G$. This number gives restrictions on the Schur multiplier of $G$ and, consequently, large classes of groups can be described. In the present paper we generalize the previous investigations on the topic, focusing on the number of elements of the form $h^m \wedge k$ of $H \wedge K$ such that $h^m \wedge k = 1_{H \wedge K}$, where $m \ge 1$ and $H$ and $K$ are arbitrary subgroups of $G$.

Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems

1999

The tangential Hilbert 16th problem is to place an upper bound for the number of isolated ovals of algebraic level curves { H ( x , y ) = const } \{H(x,y)=\operatorname {const}\} over which the integral of a polynomial 1-form P ( x , y ) d x + Q ( x , y ) d y P(x,y)\,dx+Q(x,y)\,dy (the Abelian integral) may vanish, the answer to be given in terms of the degrees n = deg ⁡ H n=\deg H and d = max ( deg ⁡ P , deg ⁡ Q ) d=\max (\deg P,\deg Q) . We describe an algorithm producing this upper bound in the form of a primitive recursive (in fact, elementary) function of n n and d d for the particular case of hyperelliptic polynomials H ( x , y ) = y 2 + U ( x ) H(x,y)=y^2+U(x) under the additional as…

General Set-Up

2017

A counterexample to Feit's Problem VIII on decomposition numbers

2016

We find a counterexample to Feit's Problem VIII on the bound of decomposition numbers. This also answers a question raised by T. Holm and W. Willems.

Induction and Character Correspondences in Groups of Odd Order

2002

Abstract Let P be a Sylow p -subgroup of G . By Irr p ′ ( G ), we denote the set of irreducible characters of G which have degree not divisible by p . When G is a solvable group of odd order, M. Isaacs constructed a natural one-to-one correspondence *:Irr p ′ ( G ) → Irr p ′ ( N G ( P )) which depends only on G and P . In this paper, we show that if ξ G  = χ ∈ Irr p ′ ( G ), then (ξ*) N G ( P )  = χ*.