مقدمه‌ای بر قضیه رادو و مسائل مرتبط

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه ریاضی محض، دانشکده علوم ریاضی، دانشگاه گیلان، رشت، گیلان، ایران

چکیده

در این مقاله، به بیان قضیۀ رادو، خانواده‌های رمزی و ارتباط آنها با نظریۀ ارگودیک و مسائل ترکیبیاتی می‌پرداریم،  همچنین تاریخچۀ پیدایش این مفاهیم از ابتدا تا چگونگی طرح و حل برخی از مسائل حوزۀ ترکیبیات و نظریۀ اعداد، به‌ویژه دیدگاه دستگاه‌های دینامیکی را  ارائه کرده و برخی از مسائل باز در این زمینه را بیان می‌کنیم.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

On Rado's theorem and its related problems

نویسندگان [English]

  • Mahmoud Mohammadzadeh Jafarabadi
  • Mohammad Akbari Tootkaboni
Department of Mathematics, University of Guilan, Rasht, Guilan, Iran
چکیده [English]

In this paper, we state Rado's theorem, Ramsey families, and their connections with ergodic theory and combinatorial problems. We discuss the historical development of these concepts since their inception to how some problems in the fields of combinatorics and number theory were formulated and solved, particularly through the lens of dynamical systems. We also address some open questions in this field.

کلیدواژه‌ها [English]

  • Rado's theorem
  • Partition regular
  • Ramsey theory
  • Stone-Cech compactification
  • Upper density
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