2017/08/21 by Lance Edward Miller, Miller, Lance Edward, W. D. Taylor +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1708.06287
openalex publication_date 2017/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article generalizes joint work of the first author and I. Swanson to the s-multiplicity recently introduced by the second author. For k a field and X = [ xi,j] a m × n-matrix of variables, we utilize Gröbner bases to give a closed form the length λ( k[X] / (I2(X) + \mathfrakm \lceil sq \rceil + \mathfrakm[q] )) where s ∈ Z[p-1], q is a sufficiently large power of p, and \mathfrakm is the homogeneous maximal ideal of k[X]. This shows this length is always eventually a \it polynomial function of q for all s.