عنوان

Introduction to lattice theory with computer science applications /

(Number (ISBN

1119069718

(Number (ISBN

9781119069713

Erroneous ISBN

1118914376

Erroneous ISBN

111906970X

Erroneous ISBN

1119069734

Erroneous ISBN

9781118914373 (cloth)

Erroneous ISBN

9781119069706

Erroneous ISBN

9781119069737

Number

dltt

Title Proper

Introduction to lattice theory with computer science applications /

General Material Designation

[Book]

First Statement of Responsibility

Vijay K. Garg

Specific Material Designation and Extent of Item

1 online resource

Text of Note

Includes bibliographical references and index

Text of Note

Introduction -- Introduction -- Relations -- Partial Orders -- Join and Meet Operations -- Operations on Posets -- Ideals and Filters -- Special Elements in Posets -- Irreducible Elements -- Dissector Elements -- Applications: Distributed Computations -- Applications: Combinatorics -- Notation and Proof Format -- Problems -- Bibliographic Remarks -- Representing Posets -- Introduction -- Labeling Elements of The Poset -- Adjacency List Representation -- Vector Clock Representation -- Matrix Representation -- Dimension-Based Representation -- Algorithms to Compute Irreducibles -- Infinite Posets -- Problems -- Bibliographic Remarks -- Dilworth's Theorem -- Introduction -- Dilworth's Theorem -- Appreciation of Dilworth's Theorem -- Dual of Dilworth's Theorem -- Generalizations of Dilworth's Theorem -- Algorithmic Perspective of Dilworth's Theorem -- Application: Hall's Marriage Theorem -- Application: Bipartite Matching -- Online Decomposition of Posets -- A Lower Bound on Online Chain Partition -- Problems -- Bibliographic Remarks -- Merging Algorithms -- Introduction -- Algorithm to Merge Chains in Vector Clock Representation -- An Upper Bound for Detecting an Aniichain of Size K -- A Lower Bound for Detecting an Antichain of Size K -- An Incremental Algorithm for Optimal Chain Decomposition -- Problems -- Bibliographic Remarks -- Lattices -- Introduction -- Sublattices -- Lattices as Algebraic Structures -- Bounding The Size of The Cover Relation of a Lattice -- Join-Irreducible Elements Revisited -- Problems -- Bibliographic Remarks -- Lattice Completion -- Introduction -- Complete Lattices -- Closure Operators -- Topped n-Structures -- Dedekind-Macneille Completion -- Structure of Dedekind-Macneille Completion of a Poset -- An Incremental Algorithm for Lattice Completion -- Breadth First Search Enumeration of Normal Cuts -- Depth First Search Enumeration of Normal Cuts -- Application: Finding the Meet and Join of Events -- Application: Detecting Global Predicates in Distributed Systems -- Application: Data Mining -- Problems -- Bibliographic Remarks -- Morphisms -- Introduction -- Lattice Homomorphism -- Lattice Isomorphism -- Lattice Congruences -- Quotient Lattice -- Lattice Homomorphism and Congruence -- Properties of Lattice Congruence Blocks -- Application: Model Checking on Reduced Lattices -- Problems -- Bibliographic Remarks -- Modular Lattices -- Introduction -- Modular Lattice -- Characterization of Modular Lattices -- Problems -- Bibliographic Remarks -- Distributive Lattices -- Introduction -- Forbidden Sublattices -- Join-Prime Elements -- Birkhoff's Representation Theorem -- Finitary Distributive Lattices -- Problems -- Bibliographic Remarks -- Slicing -- Introduction -- Representing Finite Distributive Lattices -- Predicates on Ideals -- Application: Slicing Distributed Computations -- Problems -- Bibliographic Remarks -- Applications of Slicing to Combinatorics -- Introduction -- Counting Ideals -- Boolean Algebra and Set Families -- Set Families of Size k -- Integer Partitions -- Permutations -- Problems -- Bibliographic Remarks -- Interval Orders -- Introduction -- Weak Order -- Semiorder -- Interval Order -- Problems -- Bibliographic Remarks -- Tractable Posets -- Introduction -- Series-Parallel Posets -- Two-Dimensional Posets -- Counting Ideals of a Two-Dimensional Poset -- Problems -- Bibliographic Remarks -- Enumeration Algorithms -- Introduction -- BFS Traversal -- DFS Traversal -- LEX Traversal -- Uniflow Partition of Posets -- Enumerating Tuples of Product Spaces -- Enumerating All Subsets -- Enumerating All Subsets of Size k -- Enumerating Young's Lattice -- Enumerating Permutations -- Lexical Enumeration of All Order Ideals of a Given Rank -- Problems -- Bibliographic Remarks -- Lattice of Maximal Antichains -- Introduction -- Maximal Antichain Lattice -- An Incremental Algorithm Based on Union Closure -- An Incremental Algorithm Based on BFS -- Traversal of the Lattice of Maximal Antichains -- Application: Detecting Antichain-Consistent Predicates -- Construction and Enumeration of Width Antichain Lattice -- Lexical Enumeration of Closed Sets -- Construction of Lattices Based on Union Closure -- Problems -- Bibliographic Remarks -- Dimension Theory -- Introduction -- Chain Realizers -- Standard Examples of Dimension Theory -- Relationship Between the Dimension and the Width of a Poset -- Removal Theorems for Dimension -- Critical Pairs in the Poset -- Rectangle Realizers -- Order Decomposition Method and Its Applications -- Problems -- Bibliographic Remarks -- Fixed Point Theory -- Complete Partial Orders -- Knaster-Tarski Theorem -- Application: Defining Recursion Using Fixed Points -- Problems -- Bibliographic Remarks

0

Source for Acquisition/Subscription Address

Safari Books Online

Stock Number

CL0500000671

Title

Introduction to lattice theory with computer science applications

International Standard Book Number

9781118914373

Computer science-- Mathematics.

Engineering mathematics.

Lattice theory.

COM-- 013000

COM-- 014000

COM-- 018000

COM-- 032000

COM-- 037000

COM-- 052000

COM-- 067000

Number

Edition

Class number

Garg, Vijay K., (Vijay Kumar),1963-

Ohio Library and Information Network.

Date of Transaction

20160603081241.6

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y