Linear independence of powers for polynomials

2025/07/14 by Alexandru Crăciun, Crăciun, Alexandru
Computer Science · #12E05 #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2507.10163

openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given k ≥ 2 polynomials in d ≥ 1 variables with coefficients in a field of characteristic 0, such that no two are linearly dependent, we show that for any integer r greater than max\k k-1 \choose 2, 2\, the r-th powers of the polynomials are linearly independent.

Citations

• Linear independence of powers
• On the Expressive Power of Deep Polynomial Neural Networks

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