Q -Analogs Of Identities Involving Harmonic Numbers And Binomial Coefficients,
2012
University of Haifa
Q -Analogs Of Identities Involving Harmonic Numbers And Binomial Coefficients, Toufik Mansour, Mark Shattuck, Chunwei Song
Applications and Applied Mathematics: An International Journal (AAM)
Recently, McCarthy presented two algebraic identities involving binomial coefficients and harmonic numbers, one of which generalizes an identity used to prove the Apéry number supercongruence. In 2008, Prodinger provided human proofs of identities initially obtained by Osburn and Schneider using the computer program Sigma. In this paper, we establish q -analogs of a fair number of the identities appearing in McCarthy (Integers 11 (2011): A37) and Prodinger (Integers 8 (2008): A10) by making use of q -partial fractions.
Cyclic Matching Sequencibility Of Graphs,
2012
Marshall University
Cyclic Matching Sequencibility Of Graphs, Richard A. Brualdi, Kathleen P. Kiernan, Seth A. Meyer, Michael W. Schroeder
Mathematics Faculty Research
We define the cyclic matching sequencibility of a graph to be the largest integer d such that there exists a cyclic ordering of its edges so that every d consecutive edges in the cyclic ordering form a matching. We show that the cyclic matching sequencibility of K2m and K2m+1 equals m − 1.
A Simple Bijection Between Standard 3×N Tableaux And Irreducible Webs For ����3,
2012
Smith College
A Simple Bijection Between Standard 3×N Tableaux And Irreducible Webs For ����3, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
Combinatorial spiders are a model for the invariant space of the tensor product of representations. The basic objects, webs, are certain directed planar graphs with boundary; algebraic operations on representations correspond to graph-theoretic operations on webs. Kuperberg developed spiders for rank 2 Lie algebras and ����2. Building on a result of Kuperberg’s, Khovanov-Kuperberg found a recursive algorithm giving a bijection between standard Young tableaux of shape 3 × n and irreducible webs for ����3whose boundary vertices are all sources. In this paper, we give a simple and explicit map from standard Young tableaux of shape 3 …
Liar's Domination In Grid Graphs,
2012
East Tennessee State University
Liar's Domination In Grid Graphs, Christopher Kent Sterling
Electronic Theses and Dissertations
As introduced by Slater in 2008, liar's domination provides a way of modeling protection devices where one may be faulty. Assume each vertex of a graph G is the possible location for an intruder such as a thief. A protection device at a vertex v is assumed to be able to detect the intruder at any vertex in its closed neighborhood N[v] and identify at which vertex in N[v] the intruder is located. A dominating set is required to identify any intruder's location in the graph G, and if any one device can fail to …
Preferential Arrangement Containment In Strict Superpatterns,
2012
East Tennessee State University
Preferential Arrangement Containment In Strict Superpatterns, Martha Louise Liendo
Electronic Theses and Dissertations
Most results on pattern containment deal more directly with pattern avoidance, or the enumeration and characterization of strings which avoid a given set of patterns. Little research has been conducted regarding the word size required for a word to contain all patterns of a given set of patterns. The set of patterns for which containment is sought in this thesis is the set of preferential arrangements of a given length. The term preferential arrangement denotes strings of characters in which repeated characters are allowed, but not necessary. Cardinalities for sets of all preferential arrangements of given lengths and alphabet sizes …
The Rook-Brauer Algebra,
2012
Macalester College
The Rook-Brauer Algebra, Elise G. Delmas
Mathematics, Statistics, and Computer Science Honors Projects
We introduce an associative algebra RBk(x) that has a basis of rook-Brauer diagrams. These diagrams correspond to partial matchings on 2k vertices. The rook-Brauer algebra contains the group algebra of the symmetric group, the Brauer algebra, and the rook monoid algebra as subalgebras. We show that the basis of RBk(x) is generated by special diagrams si, ti (1 <= i < k) and pj (1 <= j <= k), where the si are the simple transpositions that generated the symmetric group Sk, the ti are the "contraction maps" which generate the …
Generating Minimal Pair-Wise Covering Test Suites,
2012
Department of Computer Science, University of Texas at El Paso
Generating Minimal Pair-Wise Covering Test Suites, Luis C. Gutierrez ^, Martine Ceberio *
COURI Symposium Abstracts, Spring 2012
Software is ubiquitous and needs to be reliable. Software testing therefore plays an important role in software development. Proper testing a software system informs about its quality and reliability so as to prevent unexpected behavior during system execution. One of the methods to prevent failures consists in testing a system under different input values, but when all possible input values are tested, an impractical number of test cases might result. In software testing, pair-wise testing is a combinatorial technique which uses combination of pair input values to generate test cases. Using pair-wise testing dramatically reduces the number of test cases, …
Combinatorics Using Computational Methods,
2012
University of Nebraska-Lincoln
Combinatorics Using Computational Methods, Derrick Stolee
Department of Mathematics: Dissertations, Theses, and Student Research
Computational combinatorics involves combining pure mathematics, algorithms, and computational resources to solve problems in pure combinatorics. This thesis provides a theoretical framework for combinatorial search, which is then applied to several problems in combinatorics. Some results in space-bounded computational complexity are also presented.
The 1, 2-Conjecture For Graphs With Relatively Small Chromatic Number,
2012
University of Illinois at Urbana–Champaign
The 1, 2-Conjecture For Graphs With Relatively Small Chromatic Number, Sogol Jahanbekam, Douglas West
Faculty Publications
No abstract provided.
Exploring The On-Line Partitioning Of Posets Problem,
2012
Scripps College
Exploring The On-Line Partitioning Of Posets Problem, Leah F. Rosenbaum
Scripps Senior Theses
One question relating to partially ordered sets (posets) is that of partitioning or dividing the poset's elements into the fewest number of chains that span the poset. In 1950, Dilworth established that the width of the poset - the size of the largest set composed only of incomparable elements - is the minimum number of chains needed to partition that poset. Such a bound in on-line partitioning has been harder to establish, and work has evalutated classes of posets based on their width. This paper reviews the theorems that established val(2)=5 and illustrates them with examples. It also covers some …
Session D-3: Discrete Mathematics: A Great Curriculum Connector,
2012
Illinois Mathematics and Science Academy
Session D-3: Discrete Mathematics: A Great Curriculum Connector, Donald Porzio
Professional Learning Day
Many topics that fall under the umbrella of Discrete Mathematics cut across the traditional high school curriculum areas of algebra, geometry, and pre-calculus. Come try some classroom-ready hands-on Discrete Mathematics activities that illustrate the true interconnectedness of mathematics.
Fixed Points And Excedances In Restricted Permutations,
2012
Dartmouth College
Fixed Points And Excedances In Restricted Permutations, Sergi Elizalde
Dartmouth Scholarship
Using an unprecedented technique involving diagonals of non-rational generating functions, we prove that among the permutations of length $n$ with $i$ fixed points and $j$ excedances, the number of 321-avoiding ones equals the number of 132-avoiding ones, for any given $i,j$. Our theorem generalizes a result of Robertson, Saracino and Zeilberger. Even though bijective proofs have later been found by the author jointly with Pak and with Deutsch, this paper contains the original analytic proof that was presented at FPSAC 2003.
Complete Multipartite Graphs And The Relaxed Coloring Game,
2012
Linfield College
Complete Multipartite Graphs And The Relaxed Coloring Game, Charles Dunn
Faculty Publications
Let k be a positive integer, d be a nonnegative integer, and G be a finite graph. Two players, Alice and Bob, play a game on G by coloring the uncolored vertices with colors from a set X of k colors. At all times, the subgraph induced by a color class must have maximum degree at most d. Alice wins the game if all vertices are eventually colored; otherwise, Bob wins. The least k such that Alice has a winning strategy is called the d-relaxed game chromatic number of G, denoted χ gd (G). …
The Minimum Of The Maximum Rectilinear Crossing Numbers Of Small Cubic Graphs,
2012
Harvard University
The Minimum Of The Maximum Rectilinear Crossing Numbers Of Small Cubic Graphs, Matthew Alpert, Jens-P. Bode, Elie Feder, Heiko Harborth
Publications and Research
Here we consider the minimum of the maximum rectilinear crossing numbers for all d-regular graphs of order n. The case of connected graphs only is investigated also. For d = 3 exact values are determined for n are less than or equal to 12 and some estimations are given in general.
Semigroup As Graphs,
2012
University of New Mexico
Semigroup As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the authors study the zero divisor graph and unit graph of a semigroup. The zero divisor graphs of semigroups Zn under multiplication is studied and characterized.
Finite Factors Of Bernoulli Schemes And Distinguishing Labelings Of Directed Graphs,
2012
Sacred Heart University
Finite Factors Of Bernoulli Schemes And Distinguishing Labelings Of Directed Graphs, Andrew Lazowski, Stephen M. Shea
Mathematics Faculty Publications
A labeling of a graph is a function from the vertices of the graph to some finite set. In 1996, Albertson and Collins defined distinguishing labelings of undirected graphs. Their definition easily extends to directed graphs. Let G be a directed graph associated to the k -block presentation of a Bernoulli scheme X . We determine the automorphism group of G , and thus the distinguishing labelings of G . A labeling of G defines a finite factor of X . We define demarcating labelings and prove that demarcating labelings define finitarily Markovian finite factors of X . We use …
On A Pair Of Identities From Ramanujan's Lost Notebook,
2012
West Chester University of Pennsylvania
On A Pair Of Identities From Ramanujan's Lost Notebook, James Mclaughlin, Andrew Sills
Mathematics Faculty Publications
Using a pair of two variable series-product identities recorded by Ramanujan in the lost notebook as inspiration, we find some new identities of similar type. Each identity immediately implies an infinite family of Rogers-Ramanujan type identities, some of which are well-known identities from the literature. We also use these identities to derive some general identities for integer partitions.
Schur Functions And Their Realizations In The Slice Hyperholomorphic Setting,
2012
Chapman University
Schur Functions And Their Realizations In The Slice Hyperholomorphic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization …
On The Class Rsi Of J-Contractive Functions Intertwining Solutions Of Linear Differential Equations,
2012
Chapman University
On The Class Rsi Of J-Contractive Functions Intertwining Solutions Of Linear Differential Equations, Daniel Alpay, Andrey Melnikov, Victor Vinnikov
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we extend and solve in the class of functions RSI mentioned in the title, a number of problems originally set for the class RS of rational functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned self-adjoint matrix. The problems we consider include the Schur algorithm, the partial realization problem and the Nevanlinna-Pick interpolation problem. The arguments rely on the one-to-one correspondence between elements in a given subclass of RSI and elements in RS. Another important tool in the arguments is a new result pertaining to the classical tangential …
New Topological C-Algebras With Applications In Linear Systems Theory,
2012
Chapman University
New Topological C-Algebras With Applications In Linear Systems Theory, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
Motivated by the Schwartz space of tempered distributions S′ and the Kondratiev space of stochastic distributions S−1 we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces H′p,p∈N, with decreasing norms |⋅|p. The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form |f∗g|p≤A(p−q)|f|q|g|p for all p≥q+d, where * denotes the convolution in the monoid, A(p−q) is a strictly positive number and d is a fixed natural number (in this case we obtain commutative topological C-algebras). Such an …
