aBa Mbirika, Ph.D.

aBa Mbirika
  • Professor
  • Mathematics
Research and Creative Activities
  • Combinatorics 
  • Commutative algebra 
  • Combinatorial representation theory 
  • Algebraic combinatorics
  • Number theory
  • Lattice point geometry 
  • Graph labelings 
  • Complex reflection groups
Education
  • Ph,D., University of Iowa (Mathematics)
  • M.A., University of Iowa (Mathematics)
  • B.A., Sonoma State University (Mathematics)
Published Research

Research Publications

  1. Pell and associated Pell braid sequences as GCDs of sums of k consecutive Pell and balancing-related numbers. (Joint work with Janeè Schrader and Jürgen Spilker) -- Published by Journal of Integer Sequences, 26 No.6, Article 23.6.4 (2023), 25pp. (Available by clicking here).
  2. GCD of sums of k consecutive squares of generalized Fibonacci numbers. (Joint work with Jürgen Spilker) -- Published by Fibonacci Quarterly, 60 No.5 (2022), 255--269. (Available by clicking here).
  3. GCD of sums of k consecutive Fibonacci, Lucas, and generalized Fibonacci numbers. (Joint work with Dan Guyer) -- Published by Journal of Integer Sequences, 24 No.9, Article 21.9.8 (2021), 25pp. (Available by clicking here). (This arXiv version is easier to navigate with better numbering system).
  4. New methods to find patches of invisible integer lattice points. (Joint work with Austin Goodrich and Jasmine Nielsen) -- Published by Involve: A Journal of Mathematics, 14 No.2 (2021), 283--310. (Available by clicking here).
  5. Representation stability of Springer varieties and some combinatorial consequences. (Joint work with Julianna Tymoczko) -- Published by Journal of Algebraic Combinatorics, 53 No.3 (2021), 897--920. (Available by clicking here).
  6. An Euler phi function for the Eisenstein integers and some applications. (Joint work with Emily Gullerud) -- Published by Integers: Electronic Journal of Combinatorial Number Theory, 20, Paper No. A20 (2020), 28pp. (Available by clicking here).
  7. Lattice point visibility on generalized lines of sights. (Joint work with Edray Goins, Pamela Harris, and Bethany Kubik) -- Published by the American Mathematical Monthly, 125 No.7 (2018), 593--601. (Available by clicking here).
  8. Coprime and prime labelings of graphs. (Joint work with Adam Berliner, Nate Dean, Jonelle Hook, Alison Marr, and Cayla McBee) -- Published by Journal of Integer Sequences, 19 No.5, Article 16.5.8 (2016), 14 pp. (Available by clicking here).
  9. On the sign representations for the complex reflection groups G(r,p,n). (Joint work with Thom Pietraho and Bill Silver) -- Published by Beitrage zur Algebra und Geometrie, 57, Issue 4 (2016), 851--858, DOI 10.1007/s13366-016-0289-3, (Online published version available by clicking here).
  10. Generalizing Tanisaki's ideal via ideals of truncated symmetric functions. (Joint work with Julianna Tymoczko) -- Published by Journal of Algebraic Combinatorics, 37 (2012), 167--199. (Available by clicking here).
  11. A Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties. Published by Electronic Journal of Combinatorics, 17 No.1, Research Paper 153 (2010). (Available by clicking here).

Accepted

  • Tantalizing properties of subsequences of the Fibonacci sequence modulo 10. To appear in Rocky Mountain Journal of Mathematics. (Joint work with Dan Guyer and Miko Scott) (arXiv version available by clicking here).

Submitted

  • None at the moment.

Preprints (Almost ready to submit):[NOTE: Check my webpage for most updated versions!!!!]

  • Tridiagonal real symmetric matrices with a connection to Pascal's triangle and the Fibonacci sequence. (Joint work with Emily Gullerud and Rita Post) (arXiv version available by clicking here).

Interdisciplinary Research Publications

  • The Three Giri of Paradiso XXXIII. (Joint work with Arielle Saiber). Published by the journal, Dante Studies, 131 (2013): 237--272. (Available by clicking here).

Expository Math Writings

  • Hidden trees in the forest: On lattice points and prime labelings of graphs. This paper was inspired by my one-week residency at an AIM-NSF workshop called "Research Experiences for Undergraduate Faculty" at ICERM in Providence, RI, in June 2012. It contains some of our unpublished results, and also includes exercises and project ideas that faculty can use to involve undergraduates in research in the areas of Combinatorics, Graph Theory, and Number Theory (2012). (Available by clicking here).
  • On a coin-flip problem and its connection to pi. I wrote this with the intention of using it as a teaching (learning) tool for other faculty (students). Hence many exercises are included (2011). (Available by clicking here).
Professional Memberships

Member, American Mathematical Society -- AMS
Member, Mathematical Association of America -- MAA
Member, Project NExT Fellow (Blue 10 Dot)

Previous Professional Experience
  • Graduate Teaching Assistant at University of Iowa in Iowa City, Iowa (2004--2010)
  • Postdoctoral Fellow at Bowdoin College in Brunswick, Maine (2010--2013)