Counting Families of Mutually Intersecting Sets

Author:

Brouwer A. E.,Mills C. F.,Mills W. H.,Verbeek A.

Abstract

We show that the number of maximal intersecting families on a 9-set equals 423295099074735261880, that the number of independent sets of the Kneser graph K(9,4) equals 366996244568643864340, and that the number of intersecting families on an 8-set and on a 9-set is 14704022144627161780744368338695925293142507520 and 12553242487940503914363982718112298267975272720808010757809032705650591023015520462677475328 (roughly 1.255 . 10^91), respectively. 

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A note on the orientation covering number;Discrete Applied Mathematics;2021-12

2. q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon;International Journal of Number Theory;2019-10

3. On Mubayi's Conjecture and Conditionally Intersecting Sets;SIAM Journal on Discrete Mathematics;2018-01

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