{"paper":{"title":"A variant of the tandem duplication - random loss model of genome rearrangement","license":"","headline":"","cross_cats":["q-bio.GN"],"primary_cat":"math.CO","authors_text":"Dominique Rossin (LIAFA), Mathilde Bouvel (LIAFA)","submitted_at":"2008-01-16T16:03:05Z","abstract_excerpt":"In Soda'06, Chaudhuri, Chen, Mihaescu and Rao study algorithmic properties of the tandem duplication - random loss model of genome rearrangement, well-known in evolutionary biology. In their model, the cost of one step of duplication-loss of width k is $\\alpha^k$ for $\\alpha =1$ or $\\alpha >=2 $. In this paper, we study a variant of this model, where the cost of one step of width $k$ is 1 if $k <= K$ and $\\infty$ if $k > K$, for any value of the parameter $K in N$. We first show that permutations obtained after $p$ steps of width $K$ define classes of pattern-avoiding permutations. We also com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.2524","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"}