Current Trends on Monomial and Binomial Ideals
Historically, the study of monomial ideals became fashionable after the pioneering work by Richard Stanley in 1975 on the upper bound conjecture for spheres. On the other hand, since the early 1990s, under the strong influence of Gröbner bases, binomial ideals became gradually fashionable in commuta...
Uloženo v:
| Hlavní autoři: | , |
|---|---|
| Médium: | Online |
| Jazyk: | angličtina |
| Vydáno: |
MDPI - Multidisciplinary Digital Publishing Institute
2021
|
| Témata: | |
| On-line přístup: | 44829 |
| Tagy: |
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| _version_ | 1869517044930576384 |
|---|---|
| author | Hibi, Takayuki H |
| author_browse | H Hibi, Takayuki |
| author_facet | Hibi, Takayuki H |
| author_sort | Hibi, Takayuki |
| collection | Directory of Open Access Books |
| description | Historically, the study of monomial ideals became fashionable after the pioneering work by Richard Stanley in 1975 on the upper bound conjecture for spheres. On the other hand, since the early 1990s, under the strong influence of Gröbner bases, binomial ideals became gradually fashionable in commutative algebra. The last ten years have seen a surge of research work in the study of monomial and binomial ideals. Remarkable developments in, for example, finite free resolutions, syzygies, Hilbert functions, toric rings, as well as cohomological invariants of ordinary powers, and symbolic powers of monomial and binomial ideals, have been brought forward. The theory of monomial and binomial ideals has many benefits from combinatorics and Göbner bases. Simultaneously, monomial and binomial ideals have created new and exciting aspects of combinatorics and Göbner bases. In the present Special Issue, particular attention was paid to monomial and binomial ideals arising from combinatorial objects including finite graphs, simplicial complexes, lattice polytopes, and finite partially ordered sets, because there is a rich and intimate relationship between algebraic properties and invariants of these classes of ideals and the combinatorial structures of their combinatorial counterparts. This volume gives a brief summary of recent achievements in this area of research. It will stimulate further research that encourages breakthroughs in the theory of monomial and binomial ideals. This volume provides graduate students with fundamental materials in this research area. Furthermore, it will help researchers find exciting activities and avenues for further exploration of monomial and binomial ideals. The editors express our thanks to the contributors to the Special Issue. Funds for APC (article processing charge) were partially supported by JSPS (Japan Society for the Promotion of Science) Grants-in-Aid for Scientific Research (S) entitled ""The Birth of Modern Trends on Commutative Algebra and Convex Polytopes with Statistical and Computational Strategies"" (JP 26220701). The publication of this volume is one of the main activities of the grant. |
| format | Online |
| id | doab-20.500.12854ir-44454 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-444542023-12-20T18:40:38Z Current Trends on Monomial and Binomial Ideals Hibi, Takayuki H QA1-939 Q1-390 edge ideal flawless Cohen Macaulay dstab partially ordered set Stanley depth associated graded rings stable set polytope Stanley-Reisner ideal linear part stable set polytopes order and chain polytopes Gröbner bases distribuive lattice Cohen-Macaulay depth of powers of bipartite graphs directed cycle Rees algebra toric ideals polymatroidal ideal graph toric ring Stanley-Reisner ring Castelnuovo-Mumford regularity chain polytope complete intersection symbolic power circuit h-vector multipartite graph monomial ideal regular elements on powers of bipartite graphs syzygy projective dimension regularity Betti number (S2) condition graphs integral closure edge ring edge polytope Stanley’s inequality O-sequence algebras with straightening laws order polytope circulant graphs bipartite graph cover ideal edge ideals even cycle Castelnuovo–Mumford regularity depth colon ideals matching number Bipartite graphs bic Book Industry Communication::P Mathematics & science Historically, the study of monomial ideals became fashionable after the pioneering work by Richard Stanley in 1975 on the upper bound conjecture for spheres. On the other hand, since the early 1990s, under the strong influence of Gröbner bases, binomial ideals became gradually fashionable in commutative algebra. The last ten years have seen a surge of research work in the study of monomial and binomial ideals. Remarkable developments in, for example, finite free resolutions, syzygies, Hilbert functions, toric rings, as well as cohomological invariants of ordinary powers, and symbolic powers of monomial and binomial ideals, have been brought forward. The theory of monomial and binomial ideals has many benefits from combinatorics and Göbner bases. Simultaneously, monomial and binomial ideals have created new and exciting aspects of combinatorics and Göbner bases. In the present Special Issue, particular attention was paid to monomial and binomial ideals arising from combinatorial objects including finite graphs, simplicial complexes, lattice polytopes, and finite partially ordered sets, because there is a rich and intimate relationship between algebraic properties and invariants of these classes of ideals and the combinatorial structures of their combinatorial counterparts. This volume gives a brief summary of recent achievements in this area of research. It will stimulate further research that encourages breakthroughs in the theory of monomial and binomial ideals. This volume provides graduate students with fundamental materials in this research area. Furthermore, it will help researchers find exciting activities and avenues for further exploration of monomial and binomial ideals. The editors express our thanks to the contributors to the Special Issue. Funds for APC (article processing charge) were partially supported by JSPS (Japan Society for the Promotion of Science) Grants-in-Aid for Scientific Research (S) entitled ""The Birth of Modern Trends on Commutative Algebra and Convex Polytopes with Statistical and Computational Strategies"" (JP 26220701). The publication of this volume is one of the main activities of the grant. 2021-02-11T10:54:30Z 2021-02-11T10:54:30Z 2020-04-07 23:07:09 2020 book 44829 9783039283613 9783039283606 https://directory.doabooks.org/handle/20.500.12854/44454 eng application/octet-stream Attribution-NonCommercial-NoDerivatives 4.0 International https://mdpi.com/books/pdfview/book/2106 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-03928-361-3 10.3390/books978-3-03928-361-3 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783039283613 9783039283606 140 open access |
| spellingShingle | QA1-939 Q1-390 edge ideal flawless Cohen Macaulay dstab partially ordered set Stanley depth associated graded rings stable set polytope Stanley-Reisner ideal linear part stable set polytopes order and chain polytopes Gröbner bases distribuive lattice Cohen-Macaulay depth of powers of bipartite graphs directed cycle Rees algebra toric ideals polymatroidal ideal graph toric ring Stanley-Reisner ring Castelnuovo-Mumford regularity chain polytope complete intersection symbolic power circuit h-vector multipartite graph monomial ideal regular elements on powers of bipartite graphs syzygy projective dimension regularity Betti number (S2) condition graphs integral closure edge ring edge polytope Stanley’s inequality O-sequence algebras with straightening laws order polytope circulant graphs bipartite graph cover ideal edge ideals even cycle Castelnuovo–Mumford regularity depth colon ideals matching number Bipartite graphs bic Book Industry Communication::P Mathematics & science Hibi, Takayuki H Current Trends on Monomial and Binomial Ideals |
| title | Current Trends on Monomial and Binomial Ideals |
| title_full | Current Trends on Monomial and Binomial Ideals |
| title_fullStr | Current Trends on Monomial and Binomial Ideals |
| title_full_unstemmed | Current Trends on Monomial and Binomial Ideals |
| title_short | Current Trends on Monomial and Binomial Ideals |
| title_sort | current trends on monomial and binomial ideals |
| topic | QA1-939 Q1-390 edge ideal flawless Cohen Macaulay dstab partially ordered set Stanley depth associated graded rings stable set polytope Stanley-Reisner ideal linear part stable set polytopes order and chain polytopes Gröbner bases distribuive lattice Cohen-Macaulay depth of powers of bipartite graphs directed cycle Rees algebra toric ideals polymatroidal ideal graph toric ring Stanley-Reisner ring Castelnuovo-Mumford regularity chain polytope complete intersection symbolic power circuit h-vector multipartite graph monomial ideal regular elements on powers of bipartite graphs syzygy projective dimension regularity Betti number (S2) condition graphs integral closure edge ring edge polytope Stanley’s inequality O-sequence algebras with straightening laws order polytope circulant graphs bipartite graph cover ideal edge ideals even cycle Castelnuovo–Mumford regularity depth colon ideals matching number Bipartite graphs bic Book Industry Communication::P Mathematics & science |
| topic_facet | QA1-939 Q1-390 edge ideal flawless Cohen Macaulay dstab partially ordered set Stanley depth associated graded rings stable set polytope Stanley-Reisner ideal linear part stable set polytopes order and chain polytopes Gröbner bases distribuive lattice Cohen-Macaulay depth of powers of bipartite graphs directed cycle Rees algebra toric ideals polymatroidal ideal graph toric ring Stanley-Reisner ring Castelnuovo-Mumford regularity chain polytope complete intersection symbolic power circuit h-vector multipartite graph monomial ideal regular elements on powers of bipartite graphs syzygy projective dimension regularity Betti number (S2) condition graphs integral closure edge ring edge polytope Stanley’s inequality O-sequence algebras with straightening laws order polytope circulant graphs bipartite graph cover ideal edge ideals even cycle Castelnuovo–Mumford regularity depth colon ideals matching number Bipartite graphs bic Book Industry Communication::P Mathematics & science |
| url | 44829 |
| work_keys_str_mv | AT hibitakayuki currenttrendsonmonomialandbinomialideals AT h currenttrendsonmonomialandbinomialideals |