Extremal t-intersecting families for direct products

被引：0
作者：
Yao, Tian [1 ,2 ]
Lv, Benjian [1 ]
Wang, Kaishun [1 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China
[2] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China
来源：
DISCRETE MATHEMATICS | 2022年 / 345卷 / 11期
基金：
国家重点研发计划;
关键词：
Erdos-Ko-Rado theorem; Direct products; t -intersecting families; Cross t -intersecting families; Shifting technique; KO-RADO THEOREM; SYSTEMS;
D O I：
10.1016/j.disc.2022.113026
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, by shifting technique we study t-intersecting families for direct products where the ground set is divided into several parts. Assuming the size of each part is sufficiently large, we determine all extremal t-intersecting families for direct products. We also prove that every largest t-intersecting subfamily of a more general family introduced by Katona is trivial under certain conditions. (c) 2022 Elsevier B.V. All rights reserved.
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页数：9
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共 20 条
  • [1] The complete intersection theorem for systems of finite sets
    Ahlswede, R
    Khachatrian, LH
    [J]. EUROPEAN JOURNAL OF COMBINATORICS, 1997, 18 (02) : 125 - 136
  • [2] The intersection theorem for direct products
    Ahlswede, R
    Aydinian, H
    Khachatrian, LH
    [J]. EUROPEAN JOURNAL OF COMBINATORICS, 1998, 19 (06) : 649 - 661
  • [3] Borg P, 2008, ELECTRON J COMB, V15
  • [4] Borg P, 2014, AUSTRALAS J COMB, V60, P69
  • [5] Bresar B, 2008, AUSTRALAS J COMB, V41, P45
  • [6] INTERSECTING FAMILIES OF PERMUTATIONS
    Ellis, David
    Friedgut, Ehud
    Pilpel, Haran
    [J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 24 (03) : 649 - 682
  • [7] INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
    ERDOS, P
    RADO, R
    KO, C
    [J]. QUARTERLY JOURNAL OF MATHEMATICS, 1961, 12 (48) : 313 - &
  • [8] An Erdos-Ko-Rado theorem for direct products
    Frankl, P
    [J]. EUROPEAN JOURNAL OF COMBINATORICS, 1996, 17 (08) : 727 - 730
  • [9] Frankl P., 1978, C MATH SOC J BOLYAI, V18, P365
  • [10] A degree version of the Hilton-Milner theorem
    Frankl, Peter
    Han, Jie
    Huang, Hao
    Zhao, Yi
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2018, 155 : 493 - 502
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