邻域条件下的施赖尔集计数
Counting Schreier Sets Under Neighborhood Conditions
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中文总结 AI 辅助
该研究计数满足各类邻域条件的施赖尔集，为前四种条件确定初始计数并证明线性递推，为第五种条件证明含除数计数函数的递推关系。
中文摘要 AI 辅助
我们计数满足邻域条件的施赖尔集，包括k-聚类、k-无连续、k-邻域、k-孤立以及对整数2-平均封闭的施赖尔集。对前四种条件，我们确定初始计数并证明线性递推关系；对最后一种条件，我们证明涉及除数计数函数的递推关系。
英文摘要
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.
