J. Madden

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math.CO2017

A Generating Function for the Distribution of Runs in Binary Words

James J. Madden

Let $N (n, r, k)$ denote the number of binary words of length $n$ that begin with $0$ and contain exactly $k$ runs (i.e., maximal subwords of identical consecutive symbols) of length…

math.CO2017

Local Finiteness of Infinite Neighbor Complexes

James J. Madden

We show that if the neighbor complex, as defined by H.~Scarf, of an infinite subset of $Z^{n}$ has finite dimension, then each vertex has finitely many neighbors.