87 citations · 243 across the 20 of their papers we have counts for
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On the Local Geometry of Graphs in Terms of Their Spectra
Brice Huang, Mustazee Rahman
In this paper we consider the relation between the spectrum and the number of short cycles in large graphs. Suppose is a sequence of finite and connected gr…
A lower bound on the spectrum of unimodular networks
Mustazee Rahman
Unimodular networks are a generalization of finite graphs in a stochastic sense. We prove a lower bound to the spectral radius of the adjacency operator and of the Markov operator…
On variants of Conway and Conolly's Meta-Fibonacci recursions
Abraham Isgur, Mustazee Rahman
We study the recursions where , are integers and the superscript denotes a -fold composition, and also the recurs…
Nested Recursions, Simultaneous Parameters and Tree Superpositions
Abraham Isgur, Vitaly Kuznetsov, Mustazee Rahman +1
We apply a tree-based methodology to solve new, very broadly defined families of nested recursions of the general form R(n)=sum_{i=1}^k R(n-a_i-sum_{j=1}^p R(n-b_{ij})), where a_i…
Solving Non-homogeneous Nested Recursions Using Trees
Abraham Isgur, Mustazee Rahman, Stephen Tanny
The solutions to certain nested recursions, such as Conolly's C(n) = C(n-C(n-1))+C(n-1-C(n-2)), with initial conditions C(1)=1, C(2)=2, have a well-established combinatorial interp…
Spot-Based Generations for Meta-Fibonacci Sequences
Barnaby Dalton, Mustazee Rahman, Stephen Tanny
For many meta-Fibonacci sequences it is possible to identify a partition of the sequence into successive intervals (sometimes called blocks) with the property that the sequence beh…