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A new shift operator-based polynomial method in additive combinatorics

2023/11/15 by Sammy Luo, Luo, Sammy · 1 citation
Computer Science · Engineering · #05D40 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2311.08873

openalex publication_date 2023/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new form of the polynomial method based on what we call "shift operators," which we use to give efficient and intuitive new proofs of results previously shown using a wide range of polynomial methods, including Alon's Combinatorial Nullstellensatz and the Croot-Lev-Pach method. We end by discussing some potential new directions in which the tools introduced here may be fruitfully applied.

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