Combinatorial algorithm for the computation of cyclically standard regular bracket monomials. (March 2021)

• Record Type: Journal Article
• Authors: Nishida, Yuki; Watanabe, Sennosuke; Watanabe, Yoshihide
• Is Part Of: Journal of symbolic computation. Volume 103(2021)
• Page Start: 46
• Page End: 65
• Publication Date: 2021-03
• Subjects: Invariant theory -- Bracket polynomial -- Circular straightening law; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.10.023
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The ring of covariants of binary form is isomorphic to the ring of regular symmetric bracket polynomials in homogenized roots, which are obtained by symmetrization of regular bracket polynomials. In this paper, we give an algorithm for computing all cyclically standard bracket monomials of arbitrary degree. These monomials form a basis of the vector space of the regular bracket polynomials of a given degree. We also characterize the elemental bracket monomial of degree 2 in terms of graph theory.