Combinatorics: the Rota way
Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Cambridge
Cambridge University Press
2009
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| Schriftenreihe: | Cambridge mathematical library
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| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xii, 396 pages) |
| ISBN: | 9780511803895 |
| DOI: | 10.1017/CBO9780511803895 |
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| 505 | 8 | 0 | |t Sets, Functions, and Relations. Sets, valuations, and Boolean algebras |t Partially ordered sets |t Lattices |t Functions, partitions, and entropy |t Relations |t Matching Theory. What is matching theory? |t The marriage theorem |t Free and incidence matrices |t Submodular functions and independent matchings |t Rado's theorem on subrelations |t Doubly stochastic matrices |t The Gale-Ryser theorem |t Matching theory in higher dimensions |t Partially Ordered Sets and Lattices. Möbius functions |t Chains and antichains |t Sperner theory |t Modular and linear lattices |t Finite modular and geometric lattices |t Valuation rings and Möbius algebras |t Generating Functions and the Umbral Calculus. Generating functions |t Elementary umbral calculus |t Polynomial sequences of binomial type |t Sheffer sequences |t Umbral composition and connection matrices |t The Riemann zeta function |t Symmetric Functions and Baxter Algebras. Symmetric functions |t Distribution, occupancy, and the partition lattice |t Enumeration under a group action |t Baxter operators |t Free Baxter algebras |t Identities in Baxter algebras |t Symmetric functions over finite fields |t Historical remarks and further reading |t Determinants, Matrices, and Polynomials. Polynomials |t Apolarity |t Grace's theorem |t Multiplier sequences |t Totally positive matrices |t Exterior algebras and compound matrices |t Eigenvalues of totally positive matrices |t Variation decreasing matrices |t Pólya frequency sequences |t Selected Solutions |
| 520 | |a Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas | ||
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Datensatz im Suchindex
| _version_ | 1804176882243993600 |
|---|---|
| any_adam_object | |
| author | Kung, Joseph P. S. |
| author_GND | (DE-588)119286416 |
| author_facet | Kung, Joseph P. S. |
| author_role | aut |
| author_sort | Kung, Joseph P. S. |
| author_variant | j p s k jps jpsk |
| building | Verbundindex |
| bvnumber | BV043941028 |
| classification_rvk | SK 170 |
| collection | ZDB-20-CBO |
| contents | Sets, Functions, and Relations. Sets, valuations, and Boolean algebras Partially ordered sets Lattices Functions, partitions, and entropy Relations Matching Theory. What is matching theory? The marriage theorem Free and incidence matrices Submodular functions and independent matchings Rado's theorem on subrelations Doubly stochastic matrices The Gale-Ryser theorem Matching theory in higher dimensions Partially Ordered Sets and Lattices. Möbius functions Chains and antichains Sperner theory Modular and linear lattices Finite modular and geometric lattices Valuation rings and Möbius algebras Generating Functions and the Umbral Calculus. Generating functions Elementary umbral calculus Polynomial sequences of binomial type Sheffer sequences Umbral composition and connection matrices The Riemann zeta function Symmetric Functions and Baxter Algebras. Symmetric functions Distribution, occupancy, and the partition lattice Enumeration under a group action Baxter operators Free Baxter algebras Identities in Baxter algebras Symmetric functions over finite fields Historical remarks and further reading Determinants, Matrices, and Polynomials. Polynomials Apolarity Grace's theorem Multiplier sequences Totally positive matrices Exterior algebras and compound matrices Eigenvalues of totally positive matrices Variation decreasing matrices Pólya frequency sequences Selected Solutions |
| ctrlnum | (ZDB-20-CBO)CR9780511803895 (OCoLC)992844284 (DE-599)BVBBV043941028 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511803895 |
| format | Electronic eBook |
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| id | DE-604.BV043941028 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:14Z |
| institution | BVB |
| isbn | 9780511803895 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349997 |
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| spelling | Kung, Joseph P. S. Verfasser aut Combinatorics the Rota way Joseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan Cambridge Cambridge University Press 2009 1 online resource (xii, 396 pages) txt rdacontent c rdamedia cr rdacarrier Cambridge mathematical library Title from publisher's bibliographic system (viewed on 05 Oct 2015) Sets, Functions, and Relations. Sets, valuations, and Boolean algebras Partially ordered sets Lattices Functions, partitions, and entropy Relations Matching Theory. What is matching theory? The marriage theorem Free and incidence matrices Submodular functions and independent matchings Rado's theorem on subrelations Doubly stochastic matrices The Gale-Ryser theorem Matching theory in higher dimensions Partially Ordered Sets and Lattices. Möbius functions Chains and antichains Sperner theory Modular and linear lattices Finite modular and geometric lattices Valuation rings and Möbius algebras Generating Functions and the Umbral Calculus. Generating functions Elementary umbral calculus Polynomial sequences of binomial type Sheffer sequences Umbral composition and connection matrices The Riemann zeta function Symmetric Functions and Baxter Algebras. Symmetric functions Distribution, occupancy, and the partition lattice Enumeration under a group action Baxter operators Free Baxter algebras Identities in Baxter algebras Symmetric functions over finite fields Historical remarks and further reading Determinants, Matrices, and Polynomials. Polynomials Apolarity Grace's theorem Multiplier sequences Totally positive matrices Exterior algebras and compound matrices Eigenvalues of totally positive matrices Variation decreasing matrices Pólya frequency sequences Selected Solutions Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas Rota, Gian-Carlo / 1932-1999 Rota, Gian-Carlo 1932-1999 (DE-588)119286416 gnd rswk-swf Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd rswk-swf Rota, Gian-Carlo 1932-1999 (DE-588)119286416 p 1\p DE-604 Kombinatorik (DE-588)4031824-2 s 2\p DE-604 Rota, Gian-Carlo 1932-1999 Sonstige (DE-588)119286416 oth Yan, Catherine H. Sonstige oth Erscheint auch als Druckausgabe 978-0-521-73794-4 Erscheint auch als Druckausgabe 978-0-521-88389-4 https://doi.org/10.1017/CBO9780511803895 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kung, Joseph P. S. Combinatorics the Rota way Sets, Functions, and Relations. Sets, valuations, and Boolean algebras Partially ordered sets Lattices Functions, partitions, and entropy Relations Matching Theory. What is matching theory? The marriage theorem Free and incidence matrices Submodular functions and independent matchings Rado's theorem on subrelations Doubly stochastic matrices The Gale-Ryser theorem Matching theory in higher dimensions Partially Ordered Sets and Lattices. Möbius functions Chains and antichains Sperner theory Modular and linear lattices Finite modular and geometric lattices Valuation rings and Möbius algebras Generating Functions and the Umbral Calculus. Generating functions Elementary umbral calculus Polynomial sequences of binomial type Sheffer sequences Umbral composition and connection matrices The Riemann zeta function Symmetric Functions and Baxter Algebras. Symmetric functions Distribution, occupancy, and the partition lattice Enumeration under a group action Baxter operators Free Baxter algebras Identities in Baxter algebras Symmetric functions over finite fields Historical remarks and further reading Determinants, Matrices, and Polynomials. Polynomials Apolarity Grace's theorem Multiplier sequences Totally positive matrices Exterior algebras and compound matrices Eigenvalues of totally positive matrices Variation decreasing matrices Pólya frequency sequences Selected Solutions Rota, Gian-Carlo / 1932-1999 Rota, Gian-Carlo 1932-1999 (DE-588)119286416 gnd Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)119286416 (DE-588)4031824-2 |
| title | Combinatorics the Rota way |
| title_alt | Sets, Functions, and Relations. Sets, valuations, and Boolean algebras Partially ordered sets Lattices Functions, partitions, and entropy Relations Matching Theory. What is matching theory? The marriage theorem Free and incidence matrices Submodular functions and independent matchings Rado's theorem on subrelations Doubly stochastic matrices The Gale-Ryser theorem Matching theory in higher dimensions Partially Ordered Sets and Lattices. Möbius functions Chains and antichains Sperner theory Modular and linear lattices Finite modular and geometric lattices Valuation rings and Möbius algebras Generating Functions and the Umbral Calculus. Generating functions Elementary umbral calculus Polynomial sequences of binomial type Sheffer sequences Umbral composition and connection matrices The Riemann zeta function Symmetric Functions and Baxter Algebras. Symmetric functions Distribution, occupancy, and the partition lattice Enumeration under a group action Baxter operators Free Baxter algebras Identities in Baxter algebras Symmetric functions over finite fields Historical remarks and further reading Determinants, Matrices, and Polynomials. Polynomials Apolarity Grace's theorem Multiplier sequences Totally positive matrices Exterior algebras and compound matrices Eigenvalues of totally positive matrices Variation decreasing matrices Pólya frequency sequences Selected Solutions |
| title_auth | Combinatorics the Rota way |
| title_exact_search | Combinatorics the Rota way |
| title_full | Combinatorics the Rota way Joseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan |
| title_fullStr | Combinatorics the Rota way Joseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan |
| title_full_unstemmed | Combinatorics the Rota way Joseph P.S. Kung, Gian-Carlo Rota, Catherine H. Yan |
| title_short | Combinatorics |
| title_sort | combinatorics the rota way |
| title_sub | the Rota way |
| topic | Rota, Gian-Carlo / 1932-1999 Rota, Gian-Carlo 1932-1999 (DE-588)119286416 gnd Combinatorial analysis Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Rota, Gian-Carlo / 1932-1999 Rota, Gian-Carlo 1932-1999 Combinatorial analysis Kombinatorik |
| url | https://doi.org/10.1017/CBO9780511803895 |
| work_keys_str_mv | AT kungjosephps combinatoricstherotaway AT rotagiancarlo combinatoricstherotaway AT yancatherineh combinatoricstherotaway |