$t$-圈相交置换的 Erd\H{o}s-Ko-Rado 定理的精确界

Karen Meagher; Alison Purdy

$t$-圈相交置换的 Erd\H{o}s-Ko-Rado 定理的精确界

组合数学 2013-03-05 v2

作者: Karen Meagher , Alison Purdy

摘要

本文借鉴 Ahlswede 和 Khachatrian 在证明完整 Erd\H{o}s-Ko-Rado 定理时所使用的技术，证明了若 $n \geq 2t+1$ ，则任何两两 $t$ -圈相交的置换族的基数小于或等于 $(n-t)!$ 。此外，达到该大小的唯一族是 $t$ 个点的稳定子，即由所有具有公共 $t$ 个 1-圈的置换组成的族。这是对 Ku 和 Renshaw 先前结果的加强，并支持了 Ellis、Friedgut 和 Pilpel 最近关于 $t$ -相交置换族相应界的猜想。

关键词

Erd\H{o}s-Ko-Rado 定理置换 $t$-圈相交稳定子极值集合论组合数学

引用

@article{arxiv.1208.3638,
  title  = {The exact bound for the Erd\H{o}s-Ko-Rado theorem for $t$-cycle-intersecting permutations},
  author = {Karen Meagher and Alison Purdy},
  journal= {arXiv preprint arXiv:1208.3638},
  year   = {2013}
}

备注

23 pages; article unchanged; After v1 posted, the authors were made aware of a 2011 paper by V.M. Blinovsky which uses a similar method to give the size of the largest family for all n and t. Our article may still be of interest for its explicit characterization of the largest families, its use of generating sets and the additional background information and references

$t$-圈相交置换的 Erd\H{o}s-Ko-Rado 定理的精确界

摘要

关键词

引用

备注

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