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Ramsey theory for hypergroups

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Abstract

In this paper, Ramsey theory for discrete hypergroups is introduced with emphasis on polynomial hypergroups, discrete orbit hypergroups and hypergroup deformations of semigroups. In this context, new notions of Ramsey principle for hypergroups and \(\alpha \)-Ramsey hypergroups, \(0 \le \alpha <1,\) are defined and studied.

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Acknowledgements

The authors thank the referee for his/her kind comments and suggestions. Vishvesh Kumar thanks the Council of Scientific and Industrial Research, India, for its senior research fellowship. He thanks his supervisors Ritumoni Sarma and N. Shravan Kumar for their support. A preliminary version of a part of this paper was included in the invited talk by Ajit Iqbal Singh at the conference “The Stone–Čech compactification : Theory and Applications, at Centre for Mathematical Sciences, University of Cambridge, July 6–8 2016” in honour of Neil Hindman and Dona Strauss. She is grateful to the organizers H.G. Dales and Imre Leader for the kind invitation, hospitality and travel support. She thanks them, Dona Strauss and Neil Hindman and other participants for useful discussion. She expresses her thanks to the Indian National Science Academy for the position of INSA Emeritus Scientist and travel support. Almost half of the contributory talk given by Vishvesh Kumar at the conference “Abstract Harmonic analysis (AHA)-2018, at National Sun Yat-sen University, Kaohsiung, Taiwan, June 25–29 2018” was based on this paper. He thanks the organizers of the conference and Indian Institute of Technology Delhi for financial support. The authors thank George Willis for his useful comment and suggestion.

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Correspondence to Vishvesh Kumar.

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Communicated by Anthony To-Ming Lau.

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Kumar, V., Ross, K.A. & Singh, A.I. Ramsey theory for hypergroups. Semigroup Forum 100, 482–504 (2020). https://doi.org/10.1007/s00233-019-10009-0

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