{"paper":{"title":"Syzygy gap fractals--I. Some structural results and an upper bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Pedro Teixeira","submitted_at":"2010-08-03T15:48:58Z","abstract_excerpt":"k is a field of characteristic p>0, and l_1,...,l_n are linear forms in k[x,y]. Intending applications to Hilbert--Kunz theory, to each triple C=(F,G,H) of nonzero homogeneous elements of k[x,y] we associate a function delta_C that encodes the \"syzygy gaps\" of F^q, G^q, and H^q*l_1^{a_1}*...*l_n^{a_n}, for all q=p^e and a_i<= q. These are close relatives of functions introduced in \"p-Fractals and power series--I\" [P. Monsky, P. Teixeira, p-Fractals and power series--I. Some 2 variable results, J. Algebra 280 (2004) 505--536]. Like their relatives, the delta_C exhibit surprising self-similarity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0583","kind":"arxiv","version":1},"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"}