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You searched for subject:(Stanley Reisner ideal). Showing records 1 – 3 of 3 total matches.

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University of Kentucky

1. Stokes, Erik. THE h-VECTORS OF MATROIDS AND THE ARITHMETIC DEGREE OF SQUAREFREE STRONGLY STABLE IDEALS.

Degree: 2008, University of Kentucky

Making use of algebraic and combinatorial techniques, we study two topics: the arithmetic degree of squarefree strongly stable ideals and the h-vectors of matroid complexes. For a squarefree monomial ideal, I, the arithmetic degree of I is the number of facets of the simplicial complex which has I as its Stanley-Reisner ideal. We consider the case when I is squarefree strongly stable, in which case we give an exact formula for the arithmetic degree in terms of the minimal generators of I as well as a lower bound resembling that from the Multiplicity Conjecture. Using this, we can produce an upper bound on the number of minimal generators of any Cohen-Macaulay ideals with arbitrary codimension extending Dubreil’s theorem for codimension 2. A matroid complex is a pure complex such that every restriction is again pure. It is a long-standing open problem to classify all possible h-vectors of such complexes. In the case when the complex has dimension 1 we completely resolve this question and we give some partial results for higher dimensions. We also prove the 1-dimensional case of a conjecture of Stanley that all matroid h-vectors are pure O-sequences. Finally, we completely characterize the Stanley-Reisner ideals of matroid complexes.

Subjects/Keywords: simplicial complex; matroid; h-vector; arithmetic degree; Stanley-Reisner ideal; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Stokes, E. (2008). THE h-VECTORS OF MATROIDS AND THE ARITHMETIC DEGREE OF SQUAREFREE STRONGLY STABLE IDEALS. (Doctoral Dissertation). University of Kentucky. Retrieved from http://uknowledge.uky.edu/gradschool_diss/636

Chicago Manual of Style (16th Edition):

Stokes, Erik. “THE h-VECTORS OF MATROIDS AND THE ARITHMETIC DEGREE OF SQUAREFREE STRONGLY STABLE IDEALS.” 2008. Doctoral Dissertation, University of Kentucky. Accessed June 18, 2019. http://uknowledge.uky.edu/gradschool_diss/636.

MLA Handbook (7th Edition):

Stokes, Erik. “THE h-VECTORS OF MATROIDS AND THE ARITHMETIC DEGREE OF SQUAREFREE STRONGLY STABLE IDEALS.” 2008. Web. 18 Jun 2019.

Vancouver:

Stokes E. THE h-VECTORS OF MATROIDS AND THE ARITHMETIC DEGREE OF SQUAREFREE STRONGLY STABLE IDEALS. [Internet] [Doctoral dissertation]. University of Kentucky; 2008. [cited 2019 Jun 18]. Available from: http://uknowledge.uky.edu/gradschool_diss/636.

Council of Science Editors:

Stokes E. THE h-VECTORS OF MATROIDS AND THE ARITHMETIC DEGREE OF SQUAREFREE STRONGLY STABLE IDEALS. [Doctoral Dissertation]. University of Kentucky; 2008. Available from: http://uknowledge.uky.edu/gradschool_diss/636


Dalhousie University

2. Connon, Emma. Generalizing Fröberg's Theorem on Ideals with Linear Resolutions.

Degree: PhD, Department of Mathematics & Statistics - Math Division, 2013, Dalhousie University

In 1990, Fröberg presented a combinatorial classification of the quadratic square-free monomial ideals with linear resolutions. He showed that the edge ideal of a graph has a linear resolution if and only if the complement of the graph is chordal. Since then, a generalization of Fröberg's theorem to higher dimensions has been sought in order to classify all square-free monomial ideals with linear resolutions. Such a characterization would also give a description of all square-free monomial ideals which are Cohen-Macaulay. In this thesis we explore one method of extending Fröberg's result. We generalize the idea of a chordal graph to simplicial complexes and use simplicial homology as a bridge between this combinatorial notion and the algebraic concept of a linear resolution. We are able to give a generalization of one direction of Fröberg's theorem and, in investigating the converse direction, find a necessary and sufficient combinatorial condition for a square-free monomial ideal to have a linear resolution over fields of characteristic 2. Advisors/Committee Members: Winfried Bruns (external-examiner), Sara Faridi (graduate-coordinator), Dorette Pronk (thesis-reader), Jason Brown (thesis-reader), Sara Faridi (thesis-supervisor), Not Applicable (ethics-approval), Yes (manuscripts), Not Applicable (copyright-release).

Subjects/Keywords: monomial ideals; linear resolution; Fröberg's Theorem; chordal graph; Stanley-Reisner ideal; simplicial complex; simplicial homology

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Connon, E. (2013). Generalizing Fröberg's Theorem on Ideals with Linear Resolutions. (Doctoral Dissertation). Dalhousie University. Retrieved from http://hdl.handle.net/10222/38565

Chicago Manual of Style (16th Edition):

Connon, Emma. “Generalizing Fröberg's Theorem on Ideals with Linear Resolutions.” 2013. Doctoral Dissertation, Dalhousie University. Accessed June 18, 2019. http://hdl.handle.net/10222/38565.

MLA Handbook (7th Edition):

Connon, Emma. “Generalizing Fröberg's Theorem on Ideals with Linear Resolutions.” 2013. Web. 18 Jun 2019.

Vancouver:

Connon E. Generalizing Fröberg's Theorem on Ideals with Linear Resolutions. [Internet] [Doctoral dissertation]. Dalhousie University; 2013. [cited 2019 Jun 18]. Available from: http://hdl.handle.net/10222/38565.

Council of Science Editors:

Connon E. Generalizing Fröberg's Theorem on Ideals with Linear Resolutions. [Doctoral Dissertation]. Dalhousie University; 2013. Available from: http://hdl.handle.net/10222/38565

3. Ana Karine Rodrigues de Oliveira. Idealizadores Tangenciais e Derivações de Anéis de Stanley-Reisner.

Degree: 2012, Universidade Federal da Paraíba

A presente dissertação fornece um estudo detalhado sobre módulos de derivações logarítmicas, aqui denominados idealizadores tangenciais, bem como algumas de suas principais características. Inicialmente, várias comparações entre tais módulos são investigadas, a partir de ideais suficientemente relacionados, motivadas por um estudo prévio de Kaplansky e por sua estreita relação com a clássica teoria dos ideais diferenciais de Seidenberg. Em seguida obtém-se o primeiro resultado central, que descreve uma decomposição primária do idealizador tangencial de um ideal sem componente primária imersa. Finalmente, no segundo resultado principal, é explorada a estrutura do módulo de derivações para a classe de anéis de Stanley- Reisner, correspondendo portanto a idealizadores tangenciais de ideais monomiais. Uma aplicação de tal resultado é a resposta afirmativa para a conjectura homológica de Zariski-Lipman para a presente classe de anéis.

The present dissertation furnishes a detailed study about modules of logarithmic derivations, here dubbed tangential idealizers, and some of their main features. Initially, several comparisons between such modules are investigated starting from sufficiently related ideals, motivated by a previous study due to Kaplansky as well as by their close relationship with the classical theory of differential ideals of Seidenberg. We then obtain the first central result, which describes a primary decomposition of the tangential idealizer of an ideal without embedded primary component. Finally, in the second main result, we explore the structure of the derivation module for the class of Stanley-Reisner rings, thus corresponding to tangential idealizers of monomial ideals. An application of such a result is an affirmative answer for the homological Zariski-Lipman conjecture for the present class of rings.

Advisors/Committee Members: Cleto Brasileiro Miranda Neto.

Subjects/Keywords: anéis de Stanley-Reisner; Zariski- Lipman; ideal diagonal; idealizador tangencial; Derivação; MATEMATICA; Derivation; tangential idealizer; optimal diagonal; Zariski-Lipman; rings Stanley-Reisner

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Oliveira, A. K. R. d. (2012). Idealizadores Tangenciais e Derivações de Anéis de Stanley-Reisner. (Thesis). Universidade Federal da Paraíba. Retrieved from http://bdtd.biblioteca.ufpb.br/tde_busca/arquivo.php?codArquivo=2108

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Oliveira, Ana Karine Rodrigues de. “Idealizadores Tangenciais e Derivações de Anéis de Stanley-Reisner.” 2012. Thesis, Universidade Federal da Paraíba. Accessed June 18, 2019. http://bdtd.biblioteca.ufpb.br/tde_busca/arquivo.php?codArquivo=2108.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Oliveira, Ana Karine Rodrigues de. “Idealizadores Tangenciais e Derivações de Anéis de Stanley-Reisner.” 2012. Web. 18 Jun 2019.

Vancouver:

Oliveira AKRd. Idealizadores Tangenciais e Derivações de Anéis de Stanley-Reisner. [Internet] [Thesis]. Universidade Federal da Paraíba; 2012. [cited 2019 Jun 18]. Available from: http://bdtd.biblioteca.ufpb.br/tde_busca/arquivo.php?codArquivo=2108.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Oliveira AKRd. Idealizadores Tangenciais e Derivações de Anéis de Stanley-Reisner. [Thesis]. Universidade Federal da Paraíba; 2012. Available from: http://bdtd.biblioteca.ufpb.br/tde_busca/arquivo.php?codArquivo=2108

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.