{"paper":{"title":"Multi-state Canalyzing Functions over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Murrugarra, John O. Adeyeye, Reinhard Laubenbacher, Yuan Li","submitted_at":"2011-10-28T22:54:01Z","abstract_excerpt":"In this paper, we extend the definition of Boolean canalyzing functions to the canalyzing functions over finite field $\\mathbb{F}_{q}$, where $q$ is a power of a prime. We obtain the characterization of all the eight classes of such functions as well as their cardinality. When $q=2$, we obtain a combinatorial identity by equating our result to the formula in \\cite{Win}. Finally, for a better understanding to the magnitude, we obtain the asymptotes for all the eight cardinalities as either $n\\to\\infty$ or $q\\to\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6481","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"}