Transitive solutions of relational equations on finite sets and linear lattices

1991 ◽  
pp. 173-182 ◽  
Author(s):  
Antonio Di Nola ◽  
Waldemar Kolodziejczyk ◽  
Salvatore Sessa
Keyword(s):  
Finite Sets ◽  
Linear Lattices

scholarly journals Communication Complexity And Linearly Ordered Sets

2015 ◽  
Vol 29 (1) ◽  
pp. 93-117
Author(s):  
Mieczysław Kula ◽  
Małgorzata Serwecińska
Keyword(s):  
Upper Bound ◽  
Open Problem ◽  
Numerical Experiments ◽  
Communication Complexity ◽  
Ordered Sets ◽  
Finite Sets ◽  
The Family ◽  
Linear Lattices

AbstractThe paper is devoted to the communication complexity of lattice operations in linearly ordered finite sets. All well known techniques ([4, Chapter 1]) to determine the communication complexity of the infimum function in linear lattices disappoint, because a gap between the lower and upper bound is equal to O(log2n), where n is the cardinality of the lattice. Therefore our aim will be to investigate the communication complexity of the function more carefully. We consider a family of so called interval protocols and we construct the interval protocols for the infimum. We prove that the constructed protocols are optimal in the family of interval protocols. It is still open problem to compute the communication complexity of constructed protocols but the numerical experiments show that their complexity is less than the complexity of known protocols for the infimum function.

scholarly journals Algebraic singularities of scattering amplitudes from tropical geometry

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
James Drummond ◽  
Jack Foster ◽  
Ömer Gürdoğan ◽  
Chrysostomos Kalousios
Keyword(s):  
Scattering Amplitudes ◽  
Natural Language ◽  
Tropical Geometry ◽  
Cluster Algebras ◽  
Finite Alphabet ◽  
Square Root ◽  
Finite Sets ◽  
Yang Mills ◽  
Square Roots ◽  
Algebraic Singularities

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

scholarly journals Blind Separation for Multiple Moving Sources with Labeled Random Finite Sets

2021 ◽  
pp. 1-1
Author(s):  
Jonah Ong ◽  
Ba Tuong Vo ◽  
Sven Erik Nordholm
Keyword(s):  
Blind Separation ◽  
Finite Sets ◽  
Moving Sources ◽  
Random Finite Sets

Representation and manipulation of finite sets

1980 ◽  
Vol 10 (4) ◽  
pp. 8-12 ◽  
Author(s):  
B. L. McAllister
Keyword(s):  
Finite Sets

scholarly journals New refinements of the discrete Jensen’s inequality generated by finite or infinite permutations

2019 ◽  
Vol 94 (6) ◽  
pp. 1109-1121
Author(s):  
László Horváth
Keyword(s):  
Banach Spaces ◽  
Jensen’S Inequality ◽  
Vector Spaces ◽  
Real Vector ◽  
Finite Sets ◽  
Jensen's Inequality

AbstractIn this paper some new refinements of the discrete Jensen’s inequality are obtained in real vector spaces. The idea comes from some former refinements determined by cyclic permutations. We essentially generalize and extend these results by using permutations of finite sets and bijections of the set of positive numbers. We get refinements of the discrete Jensen’s inequality for infinite convex combinations in Banach spaces. Similar results are rare. Finally, some applications are given on different topics.

Well-quasi-ordering hereditarily finite sets

2013 ◽  
Vol 90 (6) ◽  
pp. 1278-1291 ◽  
Author(s):  
Alberto Policriti ◽  
Alexandru I. Tomescu
Keyword(s):  
Finite Sets ◽  
Quasi Ordering

Random Mappings and Decompositions of Finite Sets

1972 ◽  
Vol 17 (1) ◽  
pp. 132-145 ◽  
Author(s):  
B. A. Sevast’yanov
Keyword(s):  
Finite Sets ◽  
Random Mappings

scholarly journals Quasi-uniform Structures in Linear Lattices

1993 ◽  
Vol 23 (3) ◽  
pp. 877-884 ◽  
Author(s):  
J. Ferrer ◽  
V. Gregori ◽  
C. Alegre
Keyword(s):  
Linear Lattices

Families of finite sets with three intersections

COMBINATORICA ◽  
1984 ◽  
Vol 4 (2-3) ◽  
pp. 141-148 ◽  
Author(s):  
Peter Frankl
Keyword(s):  
Finite Sets

scholarly journals Intersection patterns of finite sets and of convex sets

2016 ◽  
Vol 145 (7) ◽  
pp. 2827-2842 ◽  
Author(s):  
Florian Frick
Keyword(s):  
Convex Sets ◽  
Finite Sets
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