Geodesic
On Finite Polarized Partition Relations
Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 321-326

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Call an m × n array an m × n; k array if its mn entries come from a set of k elements. An m × n; 1 array has mn like entries. We write (1) if every m × n; k array contains a p × q; 1 sub-array. The negation of (1) is written and means that there is an m × n; k array containing no p × q; 1 sub-array. Relations (1) are called "polarized partition relations among cardinal numbers" by P. Erdös and R. Rado [2]. In this note we prove the following theorems. 
Chvátal, V. On Finite Polarized Partition Relations. Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 321-326. doi: 10.4153/CMB-1969-040-1
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     title = {On {Finite} {Polarized} {Partition} {Relations}},
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     year = {1969},
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     doi = {10.4153/CMB-1969-040-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-040-1/}
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