2005/07/23 by Abdelmalek Abdesselam, Abdesselam, Abdelmalek, Jaydeep Chipalkatti +1
Computer Science · Mathematics · Physics and Astronomy · #13A50 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #Coding theory and cryptography #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Representation Theory (math.RT) #math.AG #math.CA #math.RT #msc:13A50 #nlin.SI
paper · pdf · doi:10.48550/arxiv.math/0507488
16 pages, LaTeX
arxiv created 2005/07/23 · openalex publication_date 2005/07/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For generic binary forms A1,...,Ar of order d we construct a class of combinants C = \\Cq: 0 ≤ q ≤ r, q ≠ 1\, to be called the Wronskian combinants of the Ai. We show that the collection C gives a projective imbedding of the Grassmannian G(r,Sd), and as a corollary, any other combinant admits a formula as an iterated transvectant in the C. Our second main result characterizes those collections of binary forms which can arise as Wronskian combinants. These collections are the ones such that an associated algebraic differential equation has the maximal number of linearly independent polynomial solutions. Along the way we deduce some identities which connect Wronskians with transvectants.