A COMBINATORIAL THEOREM ON SYSTEMS OF SETS

@inproceedings{Milner1968ACT,
  title={A COMBINATORIAL THEOREM ON SYSTEMS OF SETS},
  author={Eric C. Milner},
  year={1968}
}
It is quite easy to see that (2) and (3) give best possible results. Upper estimates for n were also given in [2] if either (Alt..., An)eS(k, </, m) and /<^(m+l) or if (Alt..., An)eS(k, I, m) and l^^(m+k), but the results in these cases are not best possible. Other results of this kind have been established in [3] and [4] which settle certain conjectures made in [2]. In this note we establish the following generalisation of Sperner's result (2). THEOREM 1. / / (A t , . . . , A„) e S(k, < w, m… CONTINUE READING
Highly Influential
This paper has highly influenced 19 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 228 citations. REVIEW CITATIONS

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 91 extracted citations

Turán problems and shadows II: Trees

J. Comb. Theory, Ser. B • 2017
View 6 Excerpts
Highly Influenced

A Canonical Ramsey Theorem for Exactly m-Coloured Complete Subgraphs

Combinatorics, Probability & Computing • 2014
View 8 Excerpts
Highly Influenced

Canonical Equivalence Relations on Qn

Order • 2003
View 5 Excerpts
Highly Influenced

Constrained Ramsey numbers of graphs

Journal of Graph Theory • 2003
View 6 Excerpts
Highly Influenced

Rainbow Generalizations of Ramsey Theory: A Survey

Graphs and Combinatorics • 2010
View 6 Excerpts
Highly Influenced

A canonical partition theorem for trees

Contributions to Discrete Mathematics • 2007
View 6 Excerpts
Highly Influenced

229 Citations

01020'81'91'02'13
Citations per Year
Semantic Scholar estimates that this publication has 229 citations based on the available data.

See our FAQ for additional information.

References

Publications referenced by this paper.
Showing 1-2 of 2 references

Some intersection theorems for systems of finite sets

A.J.W. Hilton, E. C. Milner
Quart. J. of Math. (Oxford) (2), • 1967
View 7 Excerpts
Highly Influenced

Ein Satz uber Untermengen einer endlichen

E. Sperner
Menger ", Math. Zeitschrift, • 1928
View 1 Excerpt