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Polynomial method for estimating the lower bound for the cardinality of mixed sumsets

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Abstract

We introduce the concept of mixed sumset and estimate the lower bound for its cardinality by means of the polynomial method. The result generalizes the well known Cauchy–Davenport Theorem and a theorem of Alon, Nathanson and Ruzsa regarding the lower bound for the cardinality of restricted sumsets of distinct sets in a field \(\mathbb{F}\). As a consequence of this result, we also obtain a new proof for the estimation of lower bound for the cardinality of generalized h-fold sumset modulo a prime.

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Acknowledgement

The author is very much thankful to the anonymous referees for useful comments, corrections and advice which were helpful to improve this paper.

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  1. Department of Mathematics, Indian Institute of Technology Bhilai, Raipur, 492015, India

    R. K. Mistri

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  1. R. K. Mistri
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Mistri, R.K. Polynomial method for estimating the lower bound for the cardinality of mixed sumsets. Acta Math. Hungar. 164, 331–340 (2021). https://doi.org/10.1007/s10474-021-01159-1

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  • DOI: https://doi.org/10.1007/s10474-021-01159-1

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