Real-rooted integer polynomial enumeration algorithms and interlacing polynomials via linear programming

Gary R. W. Greaves; Jeven Syatriadi

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arXiv · 2504.09241

Real-rooted integer polynomial enumeration algorithms and interlacing polynomials via linear programming

Gary R. W. Greaves·Jeven Syatriadi

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Abstract

We extend the algorithms of Robinson, Smyth, and McKee--Smyth to enumerate all real-rooted integer polynomials of a fixed degree, where the first few (at least three) leading coefficients are specified. Additionally, we introduce new linear programming algorithms to enumerate all feasible interlacing polynomials of a given polynomial that comes from a certain family of real-rooted integer polynomials. These algorithms are further specialised for the study of real equiangular lines, incorporating additional number-theoretic constraints to restrict the enumeration. Our improvements significantly enhance the efficiency of the methods presented in previous work by the authors.

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Gary R. W. Greaves, Jeven Syatriadi. 2025-04-12. Real-rooted integer polynomial enumeration algorithms and interlacing polynomials via linear programming. https://arxiv.org/abs/2504.09241

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