عنوان

Introduction to lattice theory with computer science applications /

شابک

1119069718

شابک

9781119069713

شابک اشتباه

1118914376

شابک اشتباه

111906970X

شابک اشتباه

1119069734

شابک اشتباه

9781118914373 (cloth)

شابک اشتباه

9781119069706

شابک اشتباه

9781119069737

شماره

dltt

عنوان اصلي

Introduction to lattice theory with computer science applications /

نام عام مواد

[Book]

نام نخستين پديدآور

Vijay K. Garg

نام خاص و کميت اثر

1 online resource

متن يادداشت

Includes bibliographical references and index

متن يادداشت

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

بدون عنوان

0

منبع سفارش / آدرس اشتراک

Safari Books Online

شماره انبار

CL0500000671

عنوان

Introduction to lattice theory with computer science applications

شماره استاندارد بين المللي کتاب و موسيقي

9781118914373

موضوع مستند نشده

Computer science-- Mathematics.

موضوع مستند نشده

Engineering mathematics.

موضوع مستند نشده

Lattice theory.

موضوع مستند نشده

COM-- 013000

موضوع مستند نشده

COM-- 014000

موضوع مستند نشده

COM-- 018000

موضوع مستند نشده

COM-- 032000

موضوع مستند نشده

COM-- 037000

موضوع مستند نشده

COM-- 052000

موضوع مستند نشده

COM-- 067000

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

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

مستند نام تنالگان تاييد نشده

Ohio Library and Information Network.

تاريخ عمليات

20160603081241.6

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y