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The Ramsey Properties for Grassmannians Over ℝ, ℂ

Combinatorica volume 42, pages 9–69 (2022)Cite this article

Abstract

In this note we study and obtain factorization theorems for colorings of matrices and Grassmannians over ℝ and ℂ, which can be considered metric versions of the Dual Ramsey Theorem for Boolean matrices and of the Graham-Leeb-Rothschild Theorem for Grassmannians over a finite field.

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Acknowledgments

We would like to express our gratitude to the anonymous referees for their careful review and valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Florida, PO Box 118105, Gainesville, FL, 32611, United States of America

    Dana Bartošová

  2. School of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington, 6140, New Zealand

    Martino Lupini

  3. Mathematics Department, California Institute of Technology, 1200 E. California Blvd MC 253-37, Pasadena, CA, 91125, USA

    Martino Lupini

  4. Departamento de Matemáticas Fundamentales Facultad de Ciencias, UNED, 28040, Madrid, Spain

    Jordi Lopez-Abad

  5. Collège Lionel-Groulx, 100 rue Duquet, Sainte-Therese, QC, J7E3G6, Canada

    Brice Mbombo

Authors
  1. Dana Bartošová
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  2. Jordi Lopez-Abad
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  3. Martino Lupini
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  4. Brice Mbombo
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Corresponding author

Correspondence to Jordi Lopez-Abad.

Additional information

The first author was supported by the grant FAPESP 2013/14458-9.

The second author was partially supported by the grant MTM2016-76808-P (Spain) and the Fapesp Grant 2013/24827-1 (Brazil).

The third author was partially supported by the NSF Grant DMS-1600186.

The fourth author was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) postdoctoral grant, processo 12/20084-1.

This work was initiated during a visit of J. Lopez-Abad to the Universidade de Sao Pãulo in 2014, and continued during visits of D. Bartošová and J. Lopez-Abad to the Fields Institute in the Fall 2014, a visit of M. Lupini to the Instituto de Ciencias Matemáticas in the Spring 2015, and a visit of all the authors at the Banff International Research Station in occasion of the Workshop on Homogeneous Structures in the Fall 2015. The hospitality of all these institutions is gratefully acknowledged.

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Bartošová, D., Lopez-Abad, J., Lupini, M. et al. The Ramsey Properties for Grassmannians Over ℝ, ℂ. Combinatorica 42, 9–69 (2022). https://doi.org/10.1007/s00493-020-4264-0

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  • DOI: https://doi.org/10.1007/s00493-020-4264-0

Mathematics Subject Classification (2010)

  • Primary 05D10
  • 37B05
  • Secondary 05A05
  • 46B20