From the 1 of 7 linked papers with an AI index.
7 papers
Disproofs of two conjectures concerning nondeficient numbers
John M. Campbell
The paper disproves two recent conjectures that linked nondeficient integers with {‑1,1}-perfect numbers, showing the conjectured relationships do not hold.
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{smal…
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…