An independent mathematician working  in
Pure mathematics:

Combinatorics, Number Theory,

Boolean Algebras/Propositional Logic,
Topology. 

Applied Mathematics:
Heraclitean Dialectical Concept Space, and applications

contact info:    vo1kan@hotmail.co.uk

                                                                                                                                                                                                                                                                         London, UK.

Other website: www.metricacademy.co.uk
   

Research Output in Mathematics

  0.                 Counting false entries in truth tables of bracketed formulae connected by implication (with P J Cameron) (July 2010) www.arxiv.org/abs/1106.4443

1. Catalan tree & Parity of some Sequences which are related to Catalan numbers (May 2011)  https://arxiv.org/pdf/1106.5187 

2. Counting false entries in truth tables of bracketed formulae connected by m-implication (June 2011)    http://arxiv.org/pdf/1203.4645.pdf  

3. General Combinatorical Structure of Truth Tables Connected by Implication (8-Feb 2012)  http://arxiv.org/pdf/1205.5595.pdf

4. Counting entries in Kleene Truth table. (May2020) https://arxiv.org/abs/2010.10303 

5. Notes on algebraic structure of truth tables of bracketed formulae connected by implications. (June 2021) https://arxiv.org/abs/2106.04728

6. Some divisibility properties of Jacobsthal numbers. (Dec 2022)  https://arxiv.org/pdf/2212.08814.pdf 

7. Notes on Divisibility of Catalan numbers. (Feb 2025)    https://arxiv.org/pdf/2502.04619 

8. Heraclitean Dialectical Concept Space. (Dec 2025) https://arxiv.org/abs/2601.00878 

9. Godel Implication on Finite Chains: Truth Tables and Catalan-Bracketing Enumerations. (Feb 2026)  https://arxiv.org/pdf/2602.16135 

10.  Translation Monoids and  Recursive  Evaluation in Finite Binary Algebras. (April 2026)  https://arxiv.org/abs/2604.01486 

I am an independent researcher and mathematician based in London, working in combinatorics, logic, algebraic structures, and, more recently, topology. After completing my MSci in Mathematics at Queen Mary University of London, I began working as an independent researcher.

My earlier research focused on the analysis of truth tables, particularly in multi-valued logical systems, where I studied the behaviour of bracketed formulae connected by implication. This work explored the rich combinatorial and algebraic properties that arise in such systems, especially in Kleene’s three-valued logic, which distinguishes between truth, falsity, and an indeterminate value.

A central theme of this research was the combinatorial structure of truth tables. Using recurrence relations and generating functions, I analysed these structures and showed that they can form commutative monoids, helping to clarify the algebraic foundations of a range of logical systems. This work also connected naturally with questions in theoretical computer science and discrete mathematics.

In addition, I studied divisibility properties of number sequences such as the Jacobsthal and Catalan numbers, examining how these sequences relate to logical structures and bringing together ideas from combinatorics, logic, and number theory.

My results have been presented in several papers, including preprints on arXiv, in which I developed new methods for analysing both logical and numerical systems. Alongside research, I remain deeply committed to teaching and to making advanced mathematical ideas more accessible, while fostering a broader appreciation of the subject.

More recently, I have been developing Heraclitean Dialectical Concept Space (HDCS), a mathematical framework for modelling conceptual change. This work investigates how concepts evolve, interact, and generate new concepts when existing structures break down, drawing in part on tools from topology.