Transversal theory :: an account of some aspects of combinatorial mathematics /
Transversal theory; an account of some aspects of combinatorial mathematics.
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Academic Press,
1971.
|
| Schriftenreihe: | Mathematics in science and engineering ;
v. 75. |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | Transversal theory; an account of some aspects of combinatorial mathematics. |
| Beschreibung: | 1 online resource (ix, 255 pages) |
| Bibliographie: | Includes bibliographical references (pages 236-246) and indexes. |
| ISBN: | 9780124985506 0124985505 9780080955841 0080955843 1282290436 9781282290433 |
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| 245 | 1 | 0 | |a Transversal theory : |b an account of some aspects of combinatorial mathematics / |c L. Mirsky. |
| 260 | |a New York : |b Academic Press, |c 1971. | ||
| 300 | |a 1 online resource (ix, 255 pages) | ||
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| 490 | 1 | |a Mathematics in science and engineering ; |v v. 75 | |
| 504 | |a Includes bibliographical references (pages 236-246) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a Transversal theory; an account of some aspects of combinatorial mathematics. | ||
| 505 | 0 | |a Front Cover; Transversal Theory: An account of some aspects of combinatorial mathematics; Copyright Page; Contents; Preface; Chapter 1. Sets, Topological Spaces, Graphs; 1.1 Sets and mappings; 1.2 Families; 1.3 Mapping theorems and cardinal numbers; 1.4 Boolean atoms; 1.5 The lemmas of Zorn and Tukey; 1.6 Tychonoff's theorem; 1.7 Graphs; Notes on Chapter 1; Chapter 2. Hall's Theorem and the Notion of Duality; 2.1 Transversals, representatives, and representing sets; 2.2 Proofs of the fundamental theorem for finite families; 2.3 Duality; Notes on Chapter 2 | |
| 505 | 8 | |a Chapter 3. The Method of 'Elementary Constructions'3.1 'Elementary constructions'; 3.2 Transversal index; 3.3 Further extensions of Hall's theorem; 3.4 A self-dual variant of Hall's theorem; Notes on Chapter 3; Chapter 4. Rado's Selection Principle; 4.1 Proofs of the selection principle; 4.2 Transfinite form of Hall's theorem; 4.3 A theorem of Rado and Jung; 4.4 Dilworth's decomposition theorem; 4.5 Miscellaneous applications of the selection principle; Notes on Chapter 4; Chapter 5. Variants, Refinements, and Applications of Hall's Theorem; 5.1 Disjoint partial transversals | |
| 505 | 8 | |a 5.2 Strict systems of distinct representatives5.3 Latin rectangles; 5.4 Subsets with a prescribed pattern of overlaps; Notes on Chapter 5; Chapter 6. Independent Transversals; 6.1 Pre-independence and independence; 6.2 Rado's theorem on independent transversals; 6.3 A characteristic property of independence structures; 6.4 Finite independent partial transversals; 6.5 Transversal structures and independence structures; 6.6 Marginal elements; 6.7 Axiomatic treatment of the rank function; Notes on Chapter 6; Chapter 7. Independence Structures and Linear Structures; 7.1 A hierarchy of structures | |
| 505 | 8 | |a 7.2 Bases of independence spaces7.3 Totally admissible sets; 7.4 Set-theoretic models of independence structures; Notes on Chapter 7; Chapter 8. The Rank Formula of Nash-Williams; 8.1 Sums of independence structures; 8.2 Disjoint independent sets; 8.3 A characterization of transversal structures; 8.4 Symmetrized form of Rado's theorem on independent transversals; Notes on Chapter 8; Chapter 9. Links of Two Finite Families; 9.1 The notion of a link; 9.2 Common representatives; 9.3 The criterion of Ford and Fulkerson; 9.4 Common representatives with restricted frequencies | |
| 505 | 8 | |a 9.5 An insertion theorem for common transversals9.6 Harder results for a single family; Notes on Chapter 9; Chapter 10. Links of Two Arbitrary Families; 10.1 The theorem of Mendelsohn and Dulmage and its interpretations; 10.2 Systems of representatives with repetition; 10.3 Common systems of representatives with defect; 10.4 Common transversals of two families; 10.5 Common transversals of maximal subfamilies; Notes on Chapter 10; Chapter 11. Combinatorial Properties of Matrices; 11.1 The language of matrix theory; 11.2 Theorems of König, Frobenius, and Rado | |
| 650 | 0 | |a Combinatorial analysis. |0 http://id.loc.gov/authorities/subjects/sh85028802 | |
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| _version_ | 1816881689141444608 |
| adam_text | |
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| author | Mirsky, L. (Leonid) |
| author_GND | http://id.loc.gov/authorities/names/n82054800 |
| author_facet | Mirsky, L. (Leonid) |
| author_role | |
| author_sort | Mirsky, L. |
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| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA164 |
| callnumber-raw | QA164 .M57 1971eb |
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| contents | Front Cover; Transversal Theory: An account of some aspects of combinatorial mathematics; Copyright Page; Contents; Preface; Chapter 1. Sets, Topological Spaces, Graphs; 1.1 Sets and mappings; 1.2 Families; 1.3 Mapping theorems and cardinal numbers; 1.4 Boolean atoms; 1.5 The lemmas of Zorn and Tukey; 1.6 Tychonoff's theorem; 1.7 Graphs; Notes on Chapter 1; Chapter 2. Hall's Theorem and the Notion of Duality; 2.1 Transversals, representatives, and representing sets; 2.2 Proofs of the fundamental theorem for finite families; 2.3 Duality; Notes on Chapter 2 Chapter 3. The Method of 'Elementary Constructions'3.1 'Elementary constructions'; 3.2 Transversal index; 3.3 Further extensions of Hall's theorem; 3.4 A self-dual variant of Hall's theorem; Notes on Chapter 3; Chapter 4. Rado's Selection Principle; 4.1 Proofs of the selection principle; 4.2 Transfinite form of Hall's theorem; 4.3 A theorem of Rado and Jung; 4.4 Dilworth's decomposition theorem; 4.5 Miscellaneous applications of the selection principle; Notes on Chapter 4; Chapter 5. Variants, Refinements, and Applications of Hall's Theorem; 5.1 Disjoint partial transversals 5.2 Strict systems of distinct representatives5.3 Latin rectangles; 5.4 Subsets with a prescribed pattern of overlaps; Notes on Chapter 5; Chapter 6. Independent Transversals; 6.1 Pre-independence and independence; 6.2 Rado's theorem on independent transversals; 6.3 A characteristic property of independence structures; 6.4 Finite independent partial transversals; 6.5 Transversal structures and independence structures; 6.6 Marginal elements; 6.7 Axiomatic treatment of the rank function; Notes on Chapter 6; Chapter 7. Independence Structures and Linear Structures; 7.1 A hierarchy of structures 7.2 Bases of independence spaces7.3 Totally admissible sets; 7.4 Set-theoretic models of independence structures; Notes on Chapter 7; Chapter 8. The Rank Formula of Nash-Williams; 8.1 Sums of independence structures; 8.2 Disjoint independent sets; 8.3 A characterization of transversal structures; 8.4 Symmetrized form of Rado's theorem on independent transversals; Notes on Chapter 8; Chapter 9. Links of Two Finite Families; 9.1 The notion of a link; 9.2 Common representatives; 9.3 The criterion of Ford and Fulkerson; 9.4 Common representatives with restricted frequencies 9.5 An insertion theorem for common transversals9.6 Harder results for a single family; Notes on Chapter 9; Chapter 10. Links of Two Arbitrary Families; 10.1 The theorem of Mendelsohn and Dulmage and its interpretations; 10.2 Systems of representatives with repetition; 10.3 Common systems of representatives with defect; 10.4 Common transversals of two families; 10.5 Common transversals of maximal subfamilies; Notes on Chapter 10; Chapter 11. Combinatorial Properties of Matrices; 11.1 The language of matrix theory; 11.2 Theorems of König, Frobenius, and Rado |
| ctrlnum | (OCoLC)316549564 |
| dewey-full | 511/.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.6 |
| dewey-search | 511/.6 |
| dewey-sort | 3511 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn316549564 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:42Z |
| institution | BVB |
| isbn | 9780124985506 0124985505 9780080955841 0080955843 1282290436 9781282290433 |
| language | English |
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| series | Mathematics in science and engineering ; |
| series2 | Mathematics in science and engineering ; |
| spelling | Mirsky, L. (Leonid) https://id.oclc.org/worldcat/entity/E39PBJyCJPvcyqCg8XjRtygBT3 http://id.loc.gov/authorities/names/n82054800 Transversal theory : an account of some aspects of combinatorial mathematics / L. Mirsky. New York : Academic Press, 1971. 1 online resource (ix, 255 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics in science and engineering ; v. 75 Includes bibliographical references (pages 236-246) and indexes. Print version record. Transversal theory; an account of some aspects of combinatorial mathematics. Front Cover; Transversal Theory: An account of some aspects of combinatorial mathematics; Copyright Page; Contents; Preface; Chapter 1. Sets, Topological Spaces, Graphs; 1.1 Sets and mappings; 1.2 Families; 1.3 Mapping theorems and cardinal numbers; 1.4 Boolean atoms; 1.5 The lemmas of Zorn and Tukey; 1.6 Tychonoff's theorem; 1.7 Graphs; Notes on Chapter 1; Chapter 2. Hall's Theorem and the Notion of Duality; 2.1 Transversals, representatives, and representing sets; 2.2 Proofs of the fundamental theorem for finite families; 2.3 Duality; Notes on Chapter 2 Chapter 3. The Method of 'Elementary Constructions'3.1 'Elementary constructions'; 3.2 Transversal index; 3.3 Further extensions of Hall's theorem; 3.4 A self-dual variant of Hall's theorem; Notes on Chapter 3; Chapter 4. Rado's Selection Principle; 4.1 Proofs of the selection principle; 4.2 Transfinite form of Hall's theorem; 4.3 A theorem of Rado and Jung; 4.4 Dilworth's decomposition theorem; 4.5 Miscellaneous applications of the selection principle; Notes on Chapter 4; Chapter 5. Variants, Refinements, and Applications of Hall's Theorem; 5.1 Disjoint partial transversals 5.2 Strict systems of distinct representatives5.3 Latin rectangles; 5.4 Subsets with a prescribed pattern of overlaps; Notes on Chapter 5; Chapter 6. Independent Transversals; 6.1 Pre-independence and independence; 6.2 Rado's theorem on independent transversals; 6.3 A characteristic property of independence structures; 6.4 Finite independent partial transversals; 6.5 Transversal structures and independence structures; 6.6 Marginal elements; 6.7 Axiomatic treatment of the rank function; Notes on Chapter 6; Chapter 7. Independence Structures and Linear Structures; 7.1 A hierarchy of structures 7.2 Bases of independence spaces7.3 Totally admissible sets; 7.4 Set-theoretic models of independence structures; Notes on Chapter 7; Chapter 8. The Rank Formula of Nash-Williams; 8.1 Sums of independence structures; 8.2 Disjoint independent sets; 8.3 A characterization of transversal structures; 8.4 Symmetrized form of Rado's theorem on independent transversals; Notes on Chapter 8; Chapter 9. Links of Two Finite Families; 9.1 The notion of a link; 9.2 Common representatives; 9.3 The criterion of Ford and Fulkerson; 9.4 Common representatives with restricted frequencies 9.5 An insertion theorem for common transversals9.6 Harder results for a single family; Notes on Chapter 9; Chapter 10. Links of Two Arbitrary Families; 10.1 The theorem of Mendelsohn and Dulmage and its interpretations; 10.2 Systems of representatives with repetition; 10.3 Common systems of representatives with defect; 10.4 Common transversals of two families; 10.5 Common transversals of maximal subfamilies; Notes on Chapter 10; Chapter 11. Combinatorial Properties of Matrices; 11.1 The language of matrix theory; 11.2 Theorems of König, Frobenius, and Rado Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Analyse combinatoire. MATHEMATICS Combinatorics. bisacsh Combinatorial analysis fast has work: Transversal theory (Text) https://id.oclc.org/worldcat/entity/E39PCFRkpxyCgFf3rmkTXwjmcX https://id.oclc.org/worldcat/ontology/hasWork Print version: Mirsky, L. (Leonid). Transversal theory. New York : Academic Press, 1971 9780124985506 (DLC) 71142083 (OCoLC)120443 Mathematics in science and engineering ; v. 75. http://id.loc.gov/authorities/names/n42015986 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297133 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://www.sciencedirect.com/science/bookseries/00765392/75 Volltext |
| spellingShingle | Mirsky, L. (Leonid) Transversal theory : an account of some aspects of combinatorial mathematics / Mathematics in science and engineering ; Front Cover; Transversal Theory: An account of some aspects of combinatorial mathematics; Copyright Page; Contents; Preface; Chapter 1. Sets, Topological Spaces, Graphs; 1.1 Sets and mappings; 1.2 Families; 1.3 Mapping theorems and cardinal numbers; 1.4 Boolean atoms; 1.5 The lemmas of Zorn and Tukey; 1.6 Tychonoff's theorem; 1.7 Graphs; Notes on Chapter 1; Chapter 2. Hall's Theorem and the Notion of Duality; 2.1 Transversals, representatives, and representing sets; 2.2 Proofs of the fundamental theorem for finite families; 2.3 Duality; Notes on Chapter 2 Chapter 3. The Method of 'Elementary Constructions'3.1 'Elementary constructions'; 3.2 Transversal index; 3.3 Further extensions of Hall's theorem; 3.4 A self-dual variant of Hall's theorem; Notes on Chapter 3; Chapter 4. Rado's Selection Principle; 4.1 Proofs of the selection principle; 4.2 Transfinite form of Hall's theorem; 4.3 A theorem of Rado and Jung; 4.4 Dilworth's decomposition theorem; 4.5 Miscellaneous applications of the selection principle; Notes on Chapter 4; Chapter 5. Variants, Refinements, and Applications of Hall's Theorem; 5.1 Disjoint partial transversals 5.2 Strict systems of distinct representatives5.3 Latin rectangles; 5.4 Subsets with a prescribed pattern of overlaps; Notes on Chapter 5; Chapter 6. Independent Transversals; 6.1 Pre-independence and independence; 6.2 Rado's theorem on independent transversals; 6.3 A characteristic property of independence structures; 6.4 Finite independent partial transversals; 6.5 Transversal structures and independence structures; 6.6 Marginal elements; 6.7 Axiomatic treatment of the rank function; Notes on Chapter 6; Chapter 7. Independence Structures and Linear Structures; 7.1 A hierarchy of structures 7.2 Bases of independence spaces7.3 Totally admissible sets; 7.4 Set-theoretic models of independence structures; Notes on Chapter 7; Chapter 8. The Rank Formula of Nash-Williams; 8.1 Sums of independence structures; 8.2 Disjoint independent sets; 8.3 A characterization of transversal structures; 8.4 Symmetrized form of Rado's theorem on independent transversals; Notes on Chapter 8; Chapter 9. Links of Two Finite Families; 9.1 The notion of a link; 9.2 Common representatives; 9.3 The criterion of Ford and Fulkerson; 9.4 Common representatives with restricted frequencies 9.5 An insertion theorem for common transversals9.6 Harder results for a single family; Notes on Chapter 9; Chapter 10. Links of Two Arbitrary Families; 10.1 The theorem of Mendelsohn and Dulmage and its interpretations; 10.2 Systems of representatives with repetition; 10.3 Common systems of representatives with defect; 10.4 Common transversals of two families; 10.5 Common transversals of maximal subfamilies; Notes on Chapter 10; Chapter 11. Combinatorial Properties of Matrices; 11.1 The language of matrix theory; 11.2 Theorems of König, Frobenius, and Rado Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Analyse combinatoire. MATHEMATICS Combinatorics. bisacsh Combinatorial analysis fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85028802 |
| title | Transversal theory : an account of some aspects of combinatorial mathematics / |
| title_auth | Transversal theory : an account of some aspects of combinatorial mathematics / |
| title_exact_search | Transversal theory : an account of some aspects of combinatorial mathematics / |
| title_full | Transversal theory : an account of some aspects of combinatorial mathematics / L. Mirsky. |
| title_fullStr | Transversal theory : an account of some aspects of combinatorial mathematics / L. Mirsky. |
| title_full_unstemmed | Transversal theory : an account of some aspects of combinatorial mathematics / L. Mirsky. |
| title_short | Transversal theory : |
| title_sort | transversal theory an account of some aspects of combinatorial mathematics |
| title_sub | an account of some aspects of combinatorial mathematics / |
| topic | Combinatorial analysis. http://id.loc.gov/authorities/subjects/sh85028802 Analyse combinatoire. MATHEMATICS Combinatorics. bisacsh Combinatorial analysis fast |
| topic_facet | Combinatorial analysis. Analyse combinatoire. MATHEMATICS Combinatorics. Combinatorial analysis |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=297133 https://www.sciencedirect.com/science/bookseries/00765392/75 |
| work_keys_str_mv | AT mirskyl transversaltheoryanaccountofsomeaspectsofcombinatorialmathematics |