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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

URL: http://uknowledge.uky.edu/gradschool_diss/636

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 Dubreilâ€™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 (6^{th} 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 (16^{th} 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 19, 2019. http://uknowledge.uky.edu/gradschool_diss/636.

MLA Handbook (7^{th} Edition):

Stokes, Erik. “THE h-VECTORS OF MATROIDS AND THE ARITHMETIC DEGREE OF SQUAREFREE STRONGLY STABLE IDEALS.” 2008. Web. 19 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 19]. 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

University of Florida

2. Beverage, David Gavin, 1936-. On the representation of integers by positive ternary quadratic forms.

Degree: 1962, University of Florida

URL: http://ufdc.ufl.edu/AA00056920

Subjects/Keywords: Academic degrees; Arithmetic progressions; Beverages; Degree requirements; Determinants; Genera; Graduates; Integers; Mathematical congruence; Mathematics; Forms, Quadratic; Forms, Ternary; Mathematics thesis Ph. D

Record Details Similar Records

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

APA (6^{th} Edition):

Beverage, David Gavin, 1. (1962). On the representation of integers by positive ternary quadratic forms. (Thesis). University of Florida. Retrieved from http://ufdc.ufl.edu/AA00056920

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Beverage, David Gavin, 1936-. “On the representation of integers by positive ternary quadratic forms.” 1962. Thesis, University of Florida. Accessed June 19, 2019. http://ufdc.ufl.edu/AA00056920.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Beverage, David Gavin, 1936-. “On the representation of integers by positive ternary quadratic forms.” 1962. Web. 19 Jun 2019.

Vancouver:

Beverage, David Gavin 1. On the representation of integers by positive ternary quadratic forms. [Internet] [Thesis]. University of Florida; 1962. [cited 2019 Jun 19]. Available from: http://ufdc.ufl.edu/AA00056920.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Beverage, David Gavin 1. On the representation of integers by positive ternary quadratic forms. [Thesis]. University of Florida; 1962. Available from: http://ufdc.ufl.edu/AA00056920

Not specified: Masters Thesis or Doctoral Dissertation