What question did this study set out to answer?

To introduce a new family of palindromic polynomials that lead to the generation of Salem numbers.

March 14, 2026Open Access

A New Family of Palindromic Polynomials Generating Salem Numbers

Key Points

To introduce a new family of palindromic polynomials that lead to the generation of Salem numbers.
Parameterization of polynomials by integer k ≥ 2
Utilization of an undisclosed algorithmic procedure
Verification of polynomials using SageMath
All polynomials confirmed to satisfy Salem criteria
New infinite family of palindromic polynomials identified
Polynomials rigorously checked and validated through computations

Abstract

IntroductionThis note continues a series of articles previously published on Zenodo:• “A Family of Irreducible Polynomials of Degrees 6 to 62 and Corresponding Salem Numbers”, DOI: 10.5281/zenodo.18937620;• “A Family of Salem Polynomials of Degrees 4 to 42 and Corresponding Salem Numbers”,DOI: 10.5281/zenodo.18940454.Here we exhibit another infinite family of palindromic polynomials that give rise to Salemnumbers. The family is parameterized by an integer 𝑘 ≥ 2 and is obtained through a simplealgorithmic procedure which the author prefers not to disclose at this stage; it can be madeavailable to interested researchers on request. All polynomials listed below have been rigorouslychecked with SageMath, confirming that they satisfy the Salem criteria. The computations alsobenefitted from the conversational assistance of DeepSeek.

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