Combinatorial algorithm for the computation of cyclically standard regular bracket monomials

摘要

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. (C) 2019 Elsevier Ltd. All rights reserved.