4 citations · 9 across the 9 of their papers we have counts for
10 papers
Combinations without specified separations
Michael A. Allen
We consider the restricted subsets of with being the largest member of the set of disallowed differences between subset eleme…
On a Two-Parameter Family of Generalizations of Pascal's Triangle
Michael A. Allen
We consider a two-parameter family of triangles whose -th entry (counting the initial entry as the -th entry) is the number of tilings of -boards (which are linear…
On Some Hypergeometric Supercongruence Conjectures of Long
Michael Allen
In 2003, Rodriguez Villegas conjectured 14 supercongruences between hypergeometric functions arising as periods of certain families of rigid Calabi-Yau threefolds and the Fourier c…
On Two Families of Generalizations of Pascal's Triangle
Michael A. Allen, Kenneth Edwards
We consider two families of Pascal-like triangles that have all ones on the left side and ones separated by zeros on the right side. The cases are Pascal's triangle and…
Identities involving the tribonacci numbers squared via tiling with combs
Michael A. Allen, Kenneth Edwards
The number of ways to tile an -board (an rectangular board) with -, -, and -combs is where…
Connections between two classes of generalized Fibonacci numbers squared and permanents of (0,1) Toeplitz matrices
Michael A. Allen, Kenneth Edwards
By considering the tiling of an -board (a linear array of square cells of unit width) with new types of tile that we refer to as combs, we give a combinatorial interpretatio…
New Combinatorial Interpretations of the Fibonacci Numbers Squared, Golden Rectangle Numbers, and Jacobsthal Numbers Using Two Types of Tile
Kenneth Edwards, Michael A. Allen
We consider the tiling of an -board (a board of size ) with squares of unit width and -fence tiles. A -fence tile is composed of two unit-width square su…
Existence of -Quotients For Squarefree Levels
Michael Allen
In this paper, we investigate which modular form spaces can contain -quotients, functions of the form . For even and coprime to…
A new combinatorial interpretation of the Fibonacci numbers squared
Kenneth Edwards, Michael A. Allen
We consider the tiling of an -board (a array of square cells of unit width) with half-squares ( tiles) and -fence tiles. A $(\frac…
Eta-quotients of Prime or Semiprime Level and Elliptic Curves
Michael Allen, Nicholas Anderson, Asimina Hamakiotes +2
From the Modularity Theorem proven by Wiles, Taylor, et al, we know that all elliptic curves are modular. It has been shown by Martin and Ono exactly which are represented by eta-q…