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math.CO2013★ 20 cited
Reflection factorizations of Singer cycles
Joel Brewster Lewis, Victor Reiner, Dennis Stanton
The number of shortest factorizations into reflections for a Singer cycle in GL_n(F_q) is shown to be (q^n-1)^(n - 1). Formulas counting factorizations of any length, and counting…
math.CO2013
Skyscraper Numbers
Tanya Khovanova, Joel Brewster Lewis
We introduce numbers depending on three parameters which we call skyscraper numbers. We discuss properties of these numbers and their relationship with Stirling numbers of the firs…