Topic
Covering relation
About: Covering relation is a research topic. Over the lifetime, 91 publications have been published within this topic receiving 1385 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1997
TL;DR: In this article, the authors present a generalisation of the organisation of the Book of Tournaments, including a generalised version of the game of T-Tournament, where the main solutions are defined in terms of relations between the main solution and the main problem.
Abstract: Organisation of the Book.- 1 Generalities.- 1.1 Definitions and Notations ..- 1.2 Finite Tournaments.- 1.3 Decomposition.- 1.4 Regularity.- 1.5 Useful Notions about General Binary Relations.- 2 Tournament Solutions.- 2.1 Majority Voting and Tournaments.- 2.2 Solution Concepts.- 2.3 Monotonicity, Strong Superset Property and Independence of Losers.- 2.4 Composition-Consistency and Regularity.- 2.5 Composition-Consistent Hulls.- 3 Scoring and Ranking Methods.- 3.1 Copeland Solution.- 3.2 Iterative Matrix Solutions.- 3.3 Markov Solution.- 3.4 Slater Solution.- 4 Multivariate Descriptions.- 4.1 Complete Euclidean Description.- 4.2 Multidimensional Scaling.- 5 Covering.- 5.1 Covering Relation and Uncovered Set.- 5.2 Iterations of the Uncovered Set.- 5.3 Dutta's Minimal Covering Set.- 5.4 Weak Covering a la Laffond and Laine.- 5.5 Weak Covering a la Levchenkov.- 6 Tournament Game.- 6.1 Tournament Game in Pure Strategies.- 6.2 Tournament Game in Mixed Strategies.- 6.3 Properties of the Bipartisan Set.- 6.4 Method of the Minimal Gain.- 6.5 Interpretation of Tournament Games.- 7 The Contestation Process.- 7.1 Banks' Solution.- 7.2 The Tournament Equilibrium Set.- 8 Tournament Algebras and Binary Trees.- 8.1 Definition of a Tournament Algebra.- 8.2 Binary Trees.- 8.3 An Algebraic Solution: The Top-Cycle.- 8.4 An Algebraic Solution: The Banks' set.- 8.5 Properties of Algebraic Solutions.- 9 Copeland Value of a Solution.- 9.1 Definition of the Copeland Value.- 9.2 Computation of Some Copeland Values.- 10 From Tournaments to Choice and Voting.- 10.1 Generalized Tournaments.- 10.2 Social Choice.- 10.3 Voting with Mediators.- 10.4 Voting with Agendas.- Annex - Summary Tables.- A.1 Relations between the Main Solutions.- A.2 Properties of the Main Solutions.- A.3 Games and Tournaments Concepts.- A.4 An Example.- Index of Main Notations.- References.
443 citations
TL;DR: This paper shows the lattice L"n to be isomorphic to an infimum subsemilattice under the component ordering of certain concave nondecreasing (n+1)-tuples and gives the covering relation, maximal covering number, minimal chains, infimum and supremum irreducibles, and show that partition conjugation is a lattice antiautomorphism.
184 citations
10 Jul 2016
TL;DR: An efficient representation of the partial order is derived and another partial order from the literature is combined that is independent of the underlying binary-input channel W to simplify code construction of polar codes.
Abstract: A partial order for the synthesized channels W N (i) of a polar code is presented that is independent of the underlying binary-input channel W. The partial order is based on the observation that W N (j) is stochastically degraded to W N (i) if j is obtained by swapping a more significant 1 with a less significant 0 in the binary expansion of i. We derive an efficient representation of the partial order, the so-called covering relation. The partial order is then combined with another partial order from the literature that is also independent of W. Finally, we give some remarks on how this combined partial order can be used to simplify code construction of polar codes.
167 citations
51 citations
Book•
1 Jan 1978
49 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2019 | 5 |
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 5 |
| 2015 | 5 |