A006616 Zarankiewicz's problem k_4(n). (Formerly M4998)

16, 23, 32, 43, 52, 62, 75, 87, 101, 118

Offset

4,1

Comments

a(n) is the least k such that every n X n {0,1}-matrix with k ones contains an all ones 4 X 4 submatrix. - Sean A. Irvine, May 17 2017

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=4..13.

R. K. Guy, A problem of Zarankiewicz, Research Paper No. 12, Dept. of Math., Univ. Calgary, Jan. 1967. [Annotated and scanned copy, with permission]

R. K. Guy, A many-facetted problem of Zarankiewicz, Lect. Notes Math. 110 (1969), 129-148.

Dmitry I. Ignatov, When contranominal scales give a solution to the Zarankiewicz problem?, Workshop Notes, 12th Int'l Wksp. Formal Concept Analysis Artif. Intel. (FCA4AI 2024), 27-38. See p. 34.

Formula

a(n) = n^2 - A347474(n). - Andrew Howroyd, Dec 26 2021

Crossrefs

Cf. A001197, A001198, A006626, A339635, A347474.

Sequence in context: A317380 A070572 A176657 * A225929 A179370 A166675

Adjacent sequences: A006613 A006614 A006615 * A006617 A006618 A006619

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Extensions

a(9)-a(13) from Andrew Howroyd, Dec 26 2021

Status

approved