Abstract
In this section we investigate product Ramsey theorems. Recall that the pigeonhole principle implies that if we color \(r(m - 1) + 1\) points with r many colors, then at least one color class contains m points.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Erdős, P., Rado, R.: A combinatorial theorem. J. Lond. Math. Soc. 25, 249–255 (1950)
Erdős, P., Rado, R.: A partition calculus in set theory. Bull. Am. Math. Soc. 62, 427–489 (1956)
Graham, R.L., Spencer, J.H.: A general Ramsey product theorem. Proc. Am. Math. Soc. 73, 137–139 (1979)
Meyer auf der Heide, F., Wigderson, A.: The complexity of parallel sorting. SIAM J. Comput. 16, 100–107 (1987)
Rado, R.: Direct decomposition of partitions. J. Lond. Math. Soc. 29, 71–83 (1954)
Voigt, B.: Canonizing partition theorems: diversification, products, and iterated versions. J. Comb. Theory A 40, 349–376 (1985)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Prömel, H.J. (2013). Product Theorems. In: Ramsey Theory for Discrete Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-01315-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-01315-2_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01314-5
Online ISBN: 978-3-319-01315-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)