{"paper":{"title":"The Number of Distinct Subpalindromes in Random Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.CO","authors_text":"Arseny M. Shur, Mikhail Rubinchik","submitted_at":"2015-05-29T13:47:14Z","abstract_excerpt":"We prove that a random word of length $n$ over a $k$-ary fixed alphabet contains, on expectation, $\\Theta(\\sqrt{n})$ distinct palindromic factors. We study this number of factors, $E(n,k)$, in detail, showing that the limit $\\lim_{n\\to\\infty}E(n,k)/\\sqrt{n}$ does not exist for any $k\\ge2$, $\\liminf_{n\\to\\infty}E(n,k)/\\sqrt{n}=\\Theta(1)$, and $\\limsup_{n\\to\\infty}E(n,k)/\\sqrt{n}=\\Theta(\\sqrt{k})$. Such a complicated behaviour stems from the asymmetry between the palindromes of even and odd length. We show that a similar, but much simpler, result on the expected number of squares in random words"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08043","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"}