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We prove the complete intersection theorem and the complete nontrivial-intersection theorem for systems of set partitions. This means that for all positive integers n and t we find the maximum size of a family of partitions of n-element set such that any two partitions from the family have at least t common parts and we also find the maximal size under the additional condition that no t parts appear in all members of the family.

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Complete Intersection Theorem and Complete Nontrivial Intersection Theorem for a System of Set Partitions

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  • 发表日期：

    2025年

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  • Vladimir Blinovsky

摘要

We prove the complete intersection theorem and the complete nontrivial-intersection theorem for systems of set partitions. This means that for all positive integers n and t we find the maximum size of a family of partitions of n-element set such that any two partitions from the family have at least t common parts and we also find the maximal size under the additional condition that no t parts appear in all members of the family.