Counting Schreier Sets Under Neighborhood Conditions
Ben Chen, Hung Viet Chu, Corbin F. Foss, Jie Luo, Steven J. Miller, Richard Ren, Garrett Tresch
Abstract
We count Schreier sets that satisfy a neighborhood condition, including k-clustered, k-consecutive-free, k-neighbored, k-isolated, and closed under integral 2-averages. For the first four conditions, we determine the initial counts and prove linear recurrence relations. For the last condition, we prove a recurrence that involves the divisor counting function.
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