{"paper":{"title":"$(k,\\lambda)$-Anti-Powers and Other Patterns in Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda Burcroff","submitted_at":"2018-07-20T17:31:04Z","abstract_excerpt":"Given a word, we are interested in the structure of its contiguous subwords split into $k$ blocks of equal length, especially in the homogeneous and anti-homogeneous cases. We introduce the notion of $(\\mu_1,\\dots,\\mu_k)$-block-patterns, words of the form $w = w_1\\cdots w_k$ where, when $\\{w_1,\\dots,w_k\\}$ is partitioned via equality, there are $\\mu_s$ sets of size $s$ for each $s \\in \\{1,\\dots,k\\}$. This is a generalization of the well-studied $k$-powers and the $k$-anti-powers recently introduced by Fici, Restivo, Silva, and Zamboni, as well as a refinement of the $(k,\\lambda)$-anti-powers i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07945","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"}