A. Mbirika

activity

20092025

most citedLattice point visibility on generalized lines of sight

19 citations · 31 across the 14 of their papers we have counts for

collaborators

16 papers

math.NT2025

Weighted sums of Lucas numbers of the first and second kind

aBa Mbirika

In the \textit{Fibonacci Quarterly} in 1964, C.~R.~Wall gave the following weighted sum of generalized Fibonacci numbers: $\sum_{i = 1}^{n} i G_{i} = n G_{n + 2} - G_{n + 3} + G_{3}$ , where $\…

math.NT2024

Period patterns, entry points, and orders in the Lucas sequences: theory and applications

Morgan Fiebig, aBa Mbirika, Jürgen Spilker

The goal of this paper is twofold: (1) extend theory on certain statistics in the Fibonacci and Lucas sequences modulo $m$ to the Lucas sequences $U := \left(U_n(p,q)\right)_{n \ge…

math.NT2023

Pell and associated Pell braid sequences as GCDs of sums of $k$ consecutive Pell, balancing, and related numbers

aBa Mbirika, Janee Schrader, Jürgen Spilker

We consider the greatest common divisor (GCD) of all sums of $k$ consecutive terms of a sequence $(S_{n})_{n \geq 0}$ where the terms $S_{n}$ come from exactly one of following six well…

math.NT2022

GCD of sums of $k$ consecutive squares of generalized Fibonacci numbers

aBa Mbirika, Jürgen Spilker

In 2021, Guyer and Mbirika gave two equivalent formulas that computed the greatest common divisor (GCD) of all sums of $k$ consecutive terms in the generalized Fibonacci sequence $…

math.CO2022

Tridiagonal real symmetric matrices with a connection to Pascal's triangle and the Fibonacci sequence

Emily Gullerud, Rita Johnson, aBa Mbirika

We explore a certain family ${A_{n}}_{n = 1}^{\infty}$ of $n \times n$ tridiagonal real symmetric matrices. After deriving a three-term recurrence relation for the characteristic pol…

math.NT2021

Tantalizing properties of subsequences of the Fibonacci sequence modulo 10

Dan Guyer, aBa Mbirika, Miko Scott

The Fibonacci sequence modulo $m$ , which we denote $(F_{m, n})_{n = 0}^{\infty}$ where $F_{m, n}$ is the Fibonacci number $F_{n}$ modulo $m$ , has been a well…

math.NT2021★ 2 cited

GCD of sums of $k$ consecutive Fibonacci, Lucas, and generalized Fibonacci numbers

Dan Guyer, aBa Mbirika

We explore the sums of $k$ consecutive terms in the generalized Fibonacci sequence $(G_{n})_{n \geq 0}$ given by the recurrence $G_{n} = G_{n - 1} + G_{n - 2}$ for all $n \geq 2…

math.NT2019★ 1 cited

An Euler phi function for the Eisenstein integers and some applications

Emily Gullerud, Aba Mbirika

The Euler phi function on a given integer $n$ yields the number of positive integers less than $n$ that are relatively prime to $n$ . Equivalently, it gives the order of the group o…

math.RT2018

Representation stability of the cohomology of Springer varieties and some combinatorial consequences

Aba Mbirika, Julianna Tymoczko

A sequence of $S_{n}$ -representations ${V_{n}}$ is said to be uniformly representation stable if the decomposition of $V_{n} = ⨁_{μ} c_{μ, n} V (μ)_{n}$ into irreducible representati…

math.NT2018★ 2 cited

New methods to find patches of invisible integer lattice points

Austin Goodrich, Aba Mbirika, Jasmine Nielsen

It is a surprising fact that the proportion of integer lattice points visible from the origin is exactly $\frac{6}{π ^{2}}$ , or approximately 60 percent. Hence, approximately 40 perce…

math.NT2017★ 19 cited

Lattice point visibility on generalized lines of sight

Edray Herber Goins, Pamela E. Harris, Bethany Kubik +1

For a fixed $b \in N = {1, 2, 3, \dots}$ we say that a point $(r, s)$ in the integer lattice $Z \times Z$ is $b$ -visible from the origin if it lies on the gra…

math.CO2016

Coprime and prime labelings of graphs

Adam H. Berliner, Nathaniel Dean, Jonelle Hook +3

A coprime labeling of a simple graph of order $n$ is a labeling in which adjacent vertices are given relatively prime labels, and a graph is prime if the labels used can be taken t…

math.HO2015

The three giri of Paradiso XXXIII

Arielle Saiber, Aba Mbirika

Our paper offers an analysis of how Dante describes the tre giri ("three rings") of the Holy Trinity in Paradiso 33 of the Divine Comedy. We point to the myriad possibilities Dante…

math.CO2013

On the sign representations for the complex reflection groups $G (r, p, n)$

Aba Mbirika, Thomas Pietraho, William Silver

We present a formula for the values of the sign representations of the complex reflection groups $G (r, p, n)$ in terms of its image under a generalized Robinson-Schensted map.

math.CO2010★ 7 cited

Generalizing Tanisaki's ideal via ideals of truncated symmetric functions

Aba Mbirika, Julianna Tymoczko

We define a family of ideals $I_{h}$ in the polynomial ring $Z [x_{1}, ..., x_{n}]$ that are parametrized by Hessenberg functions $h$ (equivalently Dyck paths or ample partitions).…

math.CO2009

A Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties

Aba Mbirika

The Springer variety is the set of flags stabilized by a nilpotent operator. In 1976, T.A. Springer observed that this variety's cohomology ring carries a symmetric group action, a…