{"paper":{"title":"Regular sequences of power sums and complete symmetric polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ivan Martino, Neeraj Kumar","submitted_at":"2011-10-31T14:54:11Z","abstract_excerpt":"In this article, we carry out the investigation for regular sequences of symmetric polynomials in the polynomial ring in three and four variable. Any two power sum element in $\\mathbb{C}[x_1,x_2,...,x_n]$ for $n \\geq 3$ always form a regular sequence and we state the conjecture when $p_a,p_b,p_c$ for given positive integers $a<b<c$ forms a regular sequence in $\\mathbb{C}[x_1,x_2,x_3,x_4]$. We also provide evidence for this conjecture by proving it in special instances. We also prove that any sequence of power sums of the form $p_{a}, p_{a+1},..., p_{a+ m-1},p_b$ with $m <n-1$ forms a regular s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6813","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}