1 citations · 2 across the 12 of their papers we have counts for
13 papers
Proof of Convergence of a Laplace Expansion Algorithm For Calculating Recursions Satisfied by a Family of Determinants
Russell Jay Hendel
In Evans and Hendel's recent proof of an outstanding conjecture on the resistance distances of a family of linear 3-trees, a key technique in the proof was calculating the recursio…
An Introductory Survey of Recursions in the Computation of Resistance Distance
Emily J. Evans, Russell Jay Hendel
This paper presents an introduction and expository account of a beautiful, current, and active application of recursions to the computation of resistance distance. Resistance dista…
Proof of a Conjecture on the Growth of the Maximal Resistance Distance in a Linear 3--Tree
Emily J. Evans, Russell Jay Hendel
Barret, Evans, and Francis conjectured that if is the straight linear 3-tree with vertices and is the straight linear 3-tree with vertices then \[\lim_{n\rightarr…
Runs, Squares, Palindromes, and Unbordered Factors of a Family of Binary Pattern Sequences with the All-One Pattern
Russell Jay Hendel
This paper presents results on maximal runs, order of squares, palindromes, and unbordered factors of members of the family of binary pattern sequences with the all-one pattern. Re…
Recursions Satisfied by Families of Determinants with Applications to Resistance Distance
Emily J. Evans, Russell J. Hendel
The main contribution of this paper is a six-step semi-automatic algorithm that obtains a recursion satisfied by a family of determinants by systematically and iteratively applying…
Recursions and characteristic polynomials of the Rows of the Circuit Array
Emily J. Evans, Russell J. Hendel
The 2022 Fibonacci Conference held in Sarajevo introduced the Circuit Array, a two-dimensional array associated with the resistance labels of electrical circuits whose underlying g…
An Infinite 2-Dimensional Array Associated With Electric Circuits
Emily J. Evans, Russell J. Hendel
Except for Koshy who devotes seven pages to applications of Fibonacci Numbers to electric circuits, most books and the Fibonacci Quarterly have been relatively silent on applicatio…
Resistance values under transformations in regular triangular grids
Emily J. Evans, Russell J. Hendel
In [Evans, Francis 2022; Hendel] the authors investigated resistance distance in triangular grid graphs and observed several types of asymptotic behavior. This paper extends their…
A System of Four simultaneous Recursions: Generalization of the Ledin-Shannon-Ollerton Identity
Russell Jay Hendel
This paper further generalizes a recent result of Shannon and Ollerton who resurrected an old identity due to Ledin. This paper generalizes the Ledin-Shannon-Ollerton result to all…
Limiting Behavior of Resistances in Triangular Graphs
Russell Jay Hendel
Barrett et al studied resistance labels of electrical circuits whose underlying graphs when embedded in the Cartesian plane has the form of an -grid, rows of upright triangl…
A Method for Uniformly Proving a Family of Identities
Russell Jay Hendel
This paper presents both a proof method and a result. The proof method presented is particularly suitable for uniformly proving families of identities satisfied by a family of recu…
Sums of Squares: Methods for Proving Identity Families
Russell Jay Hendel
This paper presents both a method and a result. The result presents a closed formula for the sum of the first squares of the sequence where each member is…
Recursive Triangles Appearing Embedded in Recursive Families
Russell Jay Hendel
We continue the work begun in OEIS sequence A332636 which presents recursive sequences that have triangles that appear embedded in them. This paper i) generalizes the main result p…