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arXiv · 2608.18874

Counting Schreier Sets Under Neighborhood Conditions

Ben Chen·Hung Viet Chu·Corbin F. Foss·Jie Luo·Steven J. Miller·Richard Ren·Garrett Tresch
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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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Ben Chen, Hung Viet Chu, Corbin F. Foss, Jie Luo, Steven J. Miller, Richard Ren, Garrett Tresch. 2026-08-19. Counting Schreier Sets Under Neighborhood Conditions. https://arxiv.org/abs/2608.18874

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