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Zarankiewicz's problem k_4(n,n+1).
(Formerly M5071)
+10
12
19, 27, 37, 46, 56, 68, 80, 94, 109
COMMENTS
a(n) is the least k such that every n X (n+1) {0,1}-matrix with k ones contains an all ones 4 X 4 submatrix. - Sean A. Irvine, May 18 2017
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+1) {0,1}-matrix with k ones contains an all-ones 2 X 2 submatrix.
(Formerly M3775)
+10
6
5, 8, 11, 15, 19, 23, 27, 32, 37, 43, 49, 54, 59, 64
REFERENCES
R. K. Guy, A many-facetted problem of Zarankiewicz, Lect. Notes Math. 110 (1969), 129-148.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
CROSSREFS
Cf. A006613, A006614, A006615, A006616, A006617, A006618, A006619, A006621, A006622, A006623, A006624, A006625, A006626.
A variant of Zarankiewicz's problem: a(n) is the least k such that every n X n {0,1}-matrix with k ones contains an all-ones 2 X 4 submatrix.
(Formerly M4925)
+10
4
14, 21, 26, 32, 41, 48, 56, 67
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. K. Guy, A problem of Zarankiewicz, Research Paper No. 12, Dept. of Math., Univ. Calgary, Jan. 1967. [Annotated and scanned copy, with permission]
CROSSREFS
Cf. A006613, A006615, A006616, A006617, A006618, A006619, A006620, A006621, A006622, A006623, A006624, A006625, A006626.
A variant of Zarankiewicz's problem: a(n) is the least k such that every n X n {0,1}-matrix with k ones contains an all-ones 3 X 4 submatrix.
(Formerly M4960)
+10
4
REFERENCES
R. K. Guy, A many-facetted problem of Zarankiewicz, Lect. Notes Math. 110 (1969), 129-148.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
CROSSREFS
Cf. A006613, A006614, A006616, A006617, A006618, A006619, A006620, A006621, A006622, A006623, A006624, A006625, A006626.
A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+1) {0,1}-matrix with k ones contains an all-ones 3 X 4 submatrix.
(Formerly M4826)
+10
4
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. K. Guy, A problem of Zarankiewicz, Research Paper No. 12, Dept. of Math., Univ. Calgary, Jan. 1967. [Annotated and scanned copy, with permission]
CROSSREFS
Cf. A006613, A006614, A006615, A006616, A006617, A006618, A006619, A006620, A006621, A006623, A006624, A006625, A006626.
A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+2) {0,1}-matrix with k ones contains an all-ones 3 X 4 submatrix.
(Formerly M4926)
+10
4
REFERENCES
R. K. Guy, A many-facetted problem of Zarankiewicz, Lect. Notes Math. 110 (1969), 129-148.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
CROSSREFS
Cf. A006613, A006614, A006615, A006616, A006617, A006618, A006619, A006620, A006621, A006622, A006623, A006624, A006626.
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