{"doi":"10.1093/bioinformatics/btac604","title":"A closed formula relevant to ‘Theory of local k-mer selection with applications to long-read alignment’ by Jim Shaw and Yun William Yu","abstract":"To handle the volume from next-generation sequencing data, modern sequence comparison often relies on summary sequence sketches such as minimizers, syncmers, and minimally overlapping words. Let us call an oligonucleotide of length k a k-mer. With the aim of anticipating the practical performance of a rule f that selects the k-mers in a sketch, Theorem 2 of Shaw and Yu gives a formula quantifying conservation of a sketch in the presence of a sequence mutation probability θ per base. Shaw and Yu give a four-variable recursion for computing the formula, a computation that is complicated, difficult to implement, and computationally expensive for large parameter values.For minimizers, the earliest of the k-mer sketches, this letter shows that Shaw and Yu's recursion is equivalent to a simple explicit formula. The proof of the explicit formula can be generalized, with applications to other sequence sketches likely.","journal":"Bioinformatics","year":2022,"id":291356,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":3,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9597,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2022-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":378432,"name":"John L. Spouge","orcid":"0000-0001-6207-1419","position":0,"is_corresponding":true}],"reference_count":6,"raw_metadata":null,"created_at":"2026-07-19T00:30:38.420009Z","pmid":"36063041","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}