{"paper":{"title":"Endomorphisms of regular rooted trees induced by the action of polynomials on the ring $\\mathbb Z_d$ of $d$-adic integers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Dmytro Savchuk, Elsayed Ahmed","submitted_at":"2017-11-17T21:38:49Z","abstract_excerpt":"We show that every polynomial in $\\mathbb Z[x]$ defines an endomorphism of the $d$-ary rooted tree induced by its action on the ring $\\mathbb Z_d$ of $d$-adic integers. The sections of this endomorphism also turn out to be induced by polynomials in $\\mathbb Z[x]$ of the same degree. In the case of permutational polynomials acting on $\\mathbb Z_d$ by bijections the induced endomorphisms are automorphisms of the tree. In the case of $\\mathbb Z_2$ such polynomials were completely characterized by Rivest. As our main application we utilize the result of Rivest to derive the condition on the coeffi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06735","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"}