Intersecting families in [m]ℓ∪[n]k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\begin{array}{c}{[m]}\\ \ell
Intersecting families in [m]ℓ∪[n]k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\begin{array}{c}{[m]}\\ \ell
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DOI：
10.1007/s10878-020-00648-3
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发表时间：
2020-09
影响因子：
1
通讯作者：
Jun Wang;Huajun Zhang
中科院分区：
文献类型：
--
作者：
Jun Wang;Huajun Zhang
Let m, n, ℓ m, n, ℓ and k be positive integers with ℓ ≠ k ℓ≠ k, n> 2k n> 2 k, m< 2 ℓ m< 2 ℓ and n=\max {m, n\} ≥ ℓ+ k n= max m, n≥ ℓ+ k. If F F is an intersecting family in\left () ∪\left () m ℓ∪ n k, then| F| ≤\max\left {\left (),\left ()+\left ()\right\}.| F|≤ max m ℓ, m-1 ℓ-1+ n-1 k-1. Unless n= ℓ+ k ≥ m n= ℓ+ k≥ m, equality holds if and only if\left () ≥\left () m-1 ℓ≥ n-1 k-1 and F=\left () F= m ℓ or\left () ≤\left () m-1 ℓ≤ n-1 k-1 and F F consists of all members of\left () ∪\left () m ℓ∪ n k that contain a fixed element of m ∩ n m∩ n.
