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Algebraic proof completes Colombo's difference-power determinant conjecture

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Researchers have provided an algebraic proof for Colombo's difference-power determinant conjecture, which was first proposed in 1928. The conjecture concerns the determinant of a difference-power matrix $A_d(\lambda)$, where $\lambda$ is a vector with distinct coordinates and $d$ is a natural number. The proof completes the conjecture by establishing nonsingularity for all remaining open cases, specifically supercritical odd exponents $d less n+1$. This work confirms that the rank of $A_d(\lambda)$ is equal to the minimum of $n$ and $d+1$ for all natural numbers $d$. AI

RANK_REASON This is a research paper published on arXiv detailing a mathematical proof. [lever_c_demoted from research: ic=1 ai=0.1]

Read on arXiv cs.LG →

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Algebraic proof completes Colombo's difference-power determinant conjecture

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This is a research paper published on arXiv detailing a mathematical proof. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Kun Li, Li Tie, Peng Wang, Zihan Liu ·

    An algebraic proof of Colombo's difference-power determinant conjecture

    arXiv:2608.28274v1 Announce Type: new Abstract: Let $n\ge2$ be even, let $\lambda=(\lambda_1,\ldots,\lambda_n)\in\mathbb{R}^n$ have pairwise distinct coordinates, and define the difference-power matrix \[ A_d(\lambda) := \bigl[(\lambda_r-\lambda_s)^d\bigr]_{r,s=1}^n, \qquad d\in\…

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