3 citations · 3 across the 9 of their papers we have counts for
9 papers
Disproofs of two conjectures concerning nondeficient numbers
John M. Campbell
A positive integer is said to be nondeficient if . Letting the positive divisors of a positive integer be written as $1 = d_0 < d_1 < \cdots < d_k < d_{k+1} =…
The construction of -analogues via -series and -difference equations
John M. Campbell
We apply the EKHAD-normalization method given in our recent work to obtain, via the -version of Zeilberger's algorithm, -WZ pairs such that $\sum_{k = 0}^{\infty} F(…
Quadratic irrational analogues of Ramanujan's series for
John M. Campbell, Shaun Cooper, Dongxi Ye
About 40 years ago Jonathan and Peter Borwein discovered the series identity where…
Lexical tableaux and quasisymmetric functions
John M. Campbell, Spencer Daugherty
There is a natural bijection between standard immaculate tableaux of composition shape and length and the $ \left\{ \begin{smallmatrix} n \\ k \end{smallm…
Frobenius and Verschiebung for -theory of endomorphisms
Sanjana Agarwal, Jonathan Campbell, Diego Manco +2
We show that the Frobenius and Verschiebung maps that are fundamental to Witt vectors lift to the reduced K-theory of endomorphisms. In particular, we define Frobenius and Verschie…
A generalization of Deterministic Finite Automata related to discharging
John M. Campbell
Deterministic Finite Automata (DFAs) are of central importance in automata theory. In view of how state diagrams for DFAs are defined using directed graphs, this leads us to introd…
Three-parameter generalizations of formulas due to Guillera
John M. Campbell
Guillera has introduced remarkable series expansions for of convergence rates and via the Wilf-Zeilberger method. Through an accele…
Hypergeometric accelerations with shifted indices
John M. Campbell
Chu and Zhang, in 2014, introduced hypergeometric transforms derived through the application of an Abel-type summation lemma to Dougall's -series. These transforms wer…
A generalization of immanants based on partition algebra characters
John M. Campbell
We introduce a generalization of immanants of matrices, using partition algebra characters in place of symmetric group characters. We prove that our immanant-like function on squar…