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Theoretical Limits of Language Model Alignment $f$-Divergence Regularized RLHF: Two Tales of Sampling and Unified Analyses A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models When Can Voting Help, Hurt, or Change Course? 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Some New Permutation Polynomials over Finite Fields
Nouara Zoubir, Kenza Guenda · 2017-04-30 · via cs.IT updates on arXiv.org

In this paper, we construct a new class of complete permutation monomials and several classes of permutation polynomials. Further, by giving another characterization of o-polynomials, we obtain a class of permutation polynomials of the form $G(x)+ γTr(H(x))$, where G(X) is neither a permutation nor a linearized polynomial. This is an answer to the open problem 1 of Charpin and Kyureghyan in [P. Charpin and G. Kyureghyan, When does $G(x)+ γTr(H(x))$ permute $\mathbb{F}_{p^n}$?, Finite Fields and Their Applications 15 (2009) 615--632].

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