Browse Dissertations and Theses - Mathematics by Contributor "Reznick, Bruce"

• (1991)
Let $\lbrack n\rbrack = \{1,2,\..., n\},A$ and let $2\sp{\lbrack n\rbrack}$ represent the subset lattice of (n) with sets ordered by inclusion. A collection I of subsets of (n) is called an ideal if every subset of a member ...

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• (2015-07-15)
In this thesis we study certain functions on graphs. Chapters 2 and 3 deal with variations on vertex ranking, a type of node-labeling scheme that models a parallel processing problem. A k-ranking of a graph G is a labeling ...

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• (2015-12-04)
In this thesis, we study supersaturation and enumeration problems in extremal combinatorics. In Chapter 2, with Balogh, we disprove a conjecture of Erdos and Tuza concerning the number of different ways one can create a ...

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• (2016-07-07)
In this Thesis, we consider two main themes: conditions that guarantee diverse cycle structure within a graph, and the existence of strong edge-colorings for a specific family of graphs. In Chapter 2 we consider a ...

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• (2014-05-30)
This thesis investigates various coloring problems in graph theory. Graph coloring is an essential part of combinatorics and discrete mathematics, as it deals with the fundamental problem of partitioning objects so that ...

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• (2015-01-21)
Some of the most interesting of Ramanujan's continued fraction identities are those involving ratios of Gamma functions in Chapter 12 of his second notebook. This thesis develops a method for deriving such identities, ...

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• (2010-08-20)
The main goal of this work is to improve algebraic geometric/number theoretic constructions of error-correcting codes and secret sharing schemes. For both objects we define parameters that indicate their effectiveness in ...

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• (2008)
The Prime Power Conjecture for Finite Projective Planes motivates the research that we present here. We establish a correspondence between finite affine planes and certain finite fibered loops. We prove that certain finite ...

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• (2008)
We begin by showing that minimal volume occurs if and only if the P is a lattice simplex (of dimension d ≠ 2) whose interior lattice points are collinear with a vertex of P. We then show that there can only be one such ...

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• (2014-09-16)
This is a comprehensive study of multiplicative codes of Reed-Muller type and their applications. Our codes apply to the elds of cryptography and coding theory, especially to multiparty computa- tion and secret sharing ...

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• (2018-07-13)
In this dissertation, we discuss properties of the family of sequences $\mathbf{u_d} = \{u_d(n)\}_{n \geq 0}$ for positive integer $d$. We define them by letting $u_d(n)$ be the coefficient of $X^n$ in $\displaystyle ... application/pdf PDF (2MB) • (2018-07-03) A. Lascoux and M.-P. Schutzenberger introduced Schubert polynomials to study the cohomology ring of the complete flag variety Fl(C^n). Each Schubert polynomial corresponds to the class defined by a Schubert variety X_w ... application/pdf PDF (856kB) • (2017-07-05) Suppose$f(x,y)$is a binary form of degree$d$with coefficients in a field$K \subseteq \cc$. The {\it$K$-rank of$f$} is the smallest number of$d$-th powers of linear forms over$K$of which$f$is a$K\$-linear ...

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• (2017-04-10)
A tensor product surface is the closure of the image of a rational map λ : P1 ×P1-->P3. These surfaces arise in geometric modeling and in this context it is useful to know the implicit equation of λ in P3. Currently, ...

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• (2009)
In this dissertation, we study the Tarry-Escott problem and some related diophantine systems over Z and over some quadratic fields. We give infinitely many solutions of the Tarry-Escott problem over Zi of degrees 2, ...

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