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Articles 1 - 9 of 9
Full-Text Articles in Discrete Mathematics and Combinatorics
Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard
Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard
Seaver College Research And Scholarly Achievement Symposium
We consider the problem of counting Hamiltonian cycles in circulant graphs $C^K_n$ where $n$ is the number of vertices and $K$ is a set containing elements that correspond to the allowed edges in the circulant graphs. After sorting the cycles by a topological invariant called the winding number, we use a modified transfer matrix method to convert local data into global structures. The result is a generating function that counts the number of Hamiltonian cycles in a circulant graph with $n$ vertices. The results for $K=\{1,2\}$ and $K=\{1,3\}$ have been found by previous authors. We focus on the case where …
Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard
Counting Hamiltonian Cycles In Quartic Circulant Graphs, Allison Hilliard
Seaver College Research And Scholarly Achievement Symposium
We consider the problem of counting Hamiltonian cycles in circulant graphs $C_n^{1,k}$. Our method is to partition the set of Hamiltonian cycles according to their winding numbers. Then, we construct a weighted digraph that allows us to produce a generating function that counts the number of Hamiltonian cycles for each winding number. Summing these generating functions derives a formula for the total number of Hamiltonian cycles in a circulant graph with $n$ vertices.
Influences Of Probability Instruction On Undergraduates' Understanding Of Counting Processes, Kayla Blyman
Influences Of Probability Instruction On Undergraduates' Understanding Of Counting Processes, Kayla Blyman
Theses and Dissertations--Education Sciences
Historically, students in an introductory finite mathematics course at a major university in the mid-south have struggled the most with the counting and probability unit, leading instructors to question if there was a better way to help students master the material. The purpose of this study was to begin to understand connections that undergraduate finite mathematics students are making between counting and probability. By examining student performance in counting and probability, this study provides insights that inform future instruction in courses that include counting and probability. Consequently, this study lays the groundwork for future inquiries in the field of undergraduate …
How Do I Love Thee? Let Me Count The Ways For Syllabic Variation In Certain Poetic Forms, Mike Pinter
How Do I Love Thee? Let Me Count The Ways For Syllabic Variation In Certain Poetic Forms, Mike Pinter
Journal of Humanistic Mathematics
The Dekaaz poetic form, similar to haiku with its constrained syllable counts per line, invites a connection between poetry and mathematics. Determining the number of possible Dekaaz variations leads to some interesting counting observations. We discuss two different ways to count the number of possible Dekaaz variations, one using a binary framework and the other approaching the count as an occupancy problem. The counting methods described are generalized to also count variations of other poetic forms with syllable counts specified, including haiku. We include Dekaaz examples and suggest a method that can be used to randomly generate a Dekaaz variation.
Lattice Point Counting And Height Bounds Over Number Fields And Quaternion Algebras, Lenny Fukshansky, Glenn Henshaw
Lattice Point Counting And Height Bounds Over Number Fields And Quaternion Algebras, Lenny Fukshansky, Glenn Henshaw
CMC Faculty Publications and Research
An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit applications of a particular estimate of this sort to several counting problems in number theory: counting integral points and units of bounded height over number fields, counting points of bounded height over positive definite quaternion algebras, and counting points of bounded height with a fixed support over global function fields. Our arguments use a collection of height comparison inequalities for heights over a number …
Counting The Number Of Squares Reachable In K Knight's Moves., Amanda M. Miller, David L. Farnsworth
Counting The Number Of Squares Reachable In K Knight's Moves., Amanda M. Miller, David L. Farnsworth
Articles
from its initial position on an infinite chessboard are derived. The number of squares reachable in exactly k moves are 1, 8, 32, 68, and 96 for k = 0, 1, 2, 3, and 4, respectively, and 28k – 20 for k ≥ 5. The cumulative number of squares reach- able in k or fever moves are 1, 9, 41, and 109 for k = 0, 1, 2, and 3, respectively, and 14k-squared – 6k + 5 for k ≥ 4. Although these formulas are known, the proofs that are presented are new and more mathematically accessible then preceding proofs.
Summing Cubes By Counting Rectangles, Arthur T. Benjamin, Jennifer J. Quinn, Calyssa Wurtz
Summing Cubes By Counting Rectangles, Arthur T. Benjamin, Jennifer J. Quinn, Calyssa Wurtz
All HMC Faculty Publications and Research
No abstract provided in this article.
Counting On Determinants, Arthur T. Benjamin, Naiomi T. Cameron
Counting On Determinants, Arthur T. Benjamin, Naiomi T. Cameron
All HMC Faculty Publications and Research
No abstract provided in this article.
Counting Structures In The Möbius Ladder, John P. Mcsorley
Counting Structures In The Möbius Ladder, John P. Mcsorley
Articles and Preprints
The Möbius ladder, Mn, is a simple cubic graph on 2n vertices. We present a technique which enables us to count exactly many different structures of Mn, and somewhat unifies counting in Mn. We also provide new combinatorial interpretations of some sequences, and ask some questions concerning extremal properties of cubic graphs.