scholarly journals Bonferroni-Galambos Inequalities for Partition Lattices

10.37236/1838 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Klaus Dohmen ◽  
Peter Tittmann
Keyword(s):  
Network Reliability ◽  
Partition Lattice ◽  
Bonferroni Inequalities ◽  
Uniform Hypergraphs ◽  
Negative Function ◽  
Finite Set ◽  
Partition Lattices

In this paper, we establish a new analogue of the classical Bonferroni inequalities and their improvements by Galambos for sums of type $\sum_{\pi\in {\Bbb P}(U)} (-1)^{|\pi|-1} (|\pi|-1)! f(\pi)$ where $U$ is a finite set, ${\Bbb P}(U)$ is the partition lattice of $U$ and $f:{\Bbb P}(U)\rightarrow{\Bbb R}$ is some suitable non-negative function. Applications of this new analogue are given to counting connected $k$-uniform hypergraphs, network reliability, and cumulants.

scholarly journals Grothendieck Bialgebras, Partition Lattices, and Symmetric Functions in Noncommutative Variables

10.37236/1101 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
N. Bergeron ◽  
C. Hohlweg ◽  
M. Rosas ◽  
M. Zabrocki
Keyword(s):  
Symmetric Functions ◽  
Schur Function ◽  
Partition Lattice ◽  
Partition Lattices

We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism singles out a canonical new basis of the symmetric functions in noncommutative variables which would be an analogue of the Schur function basis for this bialgebra.

scholarly journals Geometrically Constructed Bases for Homology of Non-Crossing Partition Lattices

10.37236/137 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Aisling Kenny
Keyword(s):  
Hyperplane Arrangement ◽  
Reflection Group ◽  
General Construction ◽  
Partition Lattice ◽  
Intersection Lattice ◽  
Affine Hyperplane ◽  
Partition Lattices

For any finite, real reflection group $W$, we construct a geometric basis for the homology of the corresponding non-crossing partition lattice. We relate this to the basis for the homology of the corresponding intersection lattice introduced by Björner and Wachs using a general construction of a generic affine hyperplane for the central hyperplane arrangement defined by $W$.

scholarly journals Geometrically Constructed Bases for Homology of Partition Lattices of Types $A$, $B$ and $D$

10.37236/1860 ◽  
2004 ◽  
Vol 11 (2) ◽  
Author(s):  
Anders Björner ◽  
Michelle L. Wachs
Keyword(s):  
Hyperplane Arrangement ◽  
Hyperplane Section ◽  
Hyperplane Arrangements ◽  
Proper Part ◽  
Geometric Method ◽  
Partition Lattice ◽  
General Technique ◽  
Intersection Lattice ◽  
Partition Lattices

We use the theory of hyperplane arrangements to construct natural bases for the homology of partition lattices of types $A$, $B$ and $D$. This extends and explains the "splitting basis" for the homology of the partition lattice given by M. L. Wachs, thus answering a question asked by R. Stanley. More explicitly, the following general technique is presented and utilized. Let ${\cal A}$ be a central and essential hyperplane arrangement in ${\Bbb{R}}^d$. Let $R_1,\dots,R_k$ be the bounded regions of a generic hyperplane section of ${\cal A}$. We show that there are induced polytopal cycles $\rho_{R_i}$ in the homology of the proper part $\overline{L}_{\cal A}$ of the intersection lattice such that $\{\rho_{R_i}\}_{i=1,\dots,k}$ is a basis for $\widetilde{H}_{d-2} (\overline{L}_{\cal A})$. This geometric method for constructing combinatorial homology bases is applied to the Coxeter arrangements of types $A$, $B$ and $D$, and to some interpolating arrangements.

DEVELOPMENT OF A HIGH DENSITY FINITE SET OF UNIFORM FIELD EMITTERS ON A THIN FILM GLASS SUBSTRATE

1986 ◽  
Vol 47 (C2) ◽  
pp. C2-79-C2-83
Author(s):  
G. A. KITZMANN
Keyword(s):  
Thin Film ◽  
Glass Substrate ◽  
High Density ◽  
Uniform Field ◽  
Field Emitters ◽  
Finite Set

A case study of distribution network reliability evaluation with parameter uncertainty

2014 ◽  
Author(s):  
Jianlin Yang ◽  
Yijiang Wang ◽  
Yingjun Wu ◽  
Haibo Hu ◽  
Shiyan Zuo
Keyword(s):  
Parameter Uncertainty ◽  
Network Reliability ◽  
Distribution Network ◽  
Reliability Evaluation

Subsidies Regulation Beyond the WTO

2017 ◽  
Author(s):  
Leonardo Borlini
Keyword(s):  
Trade Policy ◽  
Trade Agreements ◽  
Preferential Trade Agreements ◽  
Preferential Trade ◽  
Bilateral Agreements ◽  
Negative Function ◽  
Public Aid ◽  
The Eu

An increasingly important aspect of EU trade policy since the lifting of its self-imposed moratorium on preferential trade agreements (PTAs) has been the inclusion of WTO+ provisions on subsidies in bilateral agreements negotiated with a number of third countries. This article covers the main bilateral PTAs negotiated after the publication of the Commission’s Communication on ‘Global Europe’ in order to explore the implications of the different subsidy disciplines they set out. It also discusses the questions that arise when examining the legal discipline of public aid provided by such agreements, regarding not only the substantive appropriateness of standards and rules on compatibility, but also the procedural mechanisms designed to guarantee the implementation and the enforcement of such rules. It concludes that the most advanced among the EU PTAs are shaped as competition regulation and go beyond a mere negative function, ensuring that subsidies can contribute to fundamental public goals.

Non-repetitive sequences

1970 ◽  
Vol 68 (2) ◽  
pp. 267-274 ◽  
Author(s):  
P. A. B. Pleasants
Keyword(s):  
Repetitive Sequences ◽  
Finite Set ◽  
Infinite Sequences

This note is concerned with infinite sequences whose terms are chosen from a finite set of symbols. A segment of such a sequence is a set of one or more consecutive terms, and a repetition is a pair of finite segments that are adjacent and identical. A non-repetitive sequence is one that contains no repetitions.

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