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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…
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…
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…
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…
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…