The lattice of integer partitions
The lattice of integer partitions
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DOI：
10.1016/0012-365x(73)90094-0
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发表时间：
1973
期刊：
影响因子：
--
通讯作者：
Tom Brylawski
中科院分区：
文献类型：
--
作者：
Tom Brylawski
在本文中，我们研究了按优势排序的整数的latticeLnof 划分。我们证明在某些凹非递减 (n+1) 元组的分量排序下，Ln 与下确界亚半格同构。对于Ln，给出覆盖关系、最大覆盖数、最小链、不可约下确界和上界、链条件、区分区间；并证明配分共轭是格子反自同构。Ln 证明不存在具有五个元素且秩为二的子格，并且我们表征了由两个 cocovers 生成的区间。莫比乌斯函数 Lnis 计算并显示为 0,1 或 -1。然后，我们给出研究具有规定行和列和的 (0,1) 矩阵类的方法，并计算它们基数的下界。
In this paper we study the latticeLnof partitions of an integernordered by dominance. We showLnto be isomorphic to an infimum subsemilattice under the component ordering of certain concave nondecreasing (n+1)-tuples. ForLn, we give the covering relation, maximal covering number, minimal chains, infimum and supremum irreducibles, a chain condition, distinguished intervals; and show that partition conjugation is a lattice antiautomorphism.Lnis shown to have no sublattice having five elements and rank two, and we characterize intervals generated by two cocovers. The Möbius function ofLnis computed and shown to be 0,1 or -1. We then give methods for studying classes of (0,1)-matrices with prescribed row and column sums and compute a lower bound for their cardinalities.