{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T20:33:16Z","timestamp":1773433996537,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,2,5]],"date-time":"2019-02-05T00:00:00Z","timestamp":1549324800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,2,5]],"date-time":"2019-02-05T00:00:00Z","timestamp":1549324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,2,5]],"date-time":"2019-02-05T00:00:00Z","timestamp":1549324800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-associative law (equivalently, right rotation). We establish a focusing property for this sequent calculus (a strengthening of cut-elimination), which yields the following coherence theorem: every valid entailment in the Tamari order has exactly one focused derivation. We then describe two main applications of the coherence theorem, including: 1. A new proof of the lattice property for the Tamari order, and 2. A new proof of the Tutte-Chapoton formula for the number of intervals in the Tamari lattice $Y_n$.<\/jats:p>\n                  <jats:p>Comment: This article is an extended version of a paper presented at FSCD   2017. [v2: minor rev] arXiv admin note: text overlap with arXiv:1701.02917<\/jats:p>","DOI":"10.23638\/lmcs-15(1:9)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T13:37:04Z","timestamp":1743687424000},"source":"Crossref","is-referenced-by-count":3,"title":["A sequent calculus for a semi-associative law"],"prefix":"10.23638","volume":"Volume 15, Issue 1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5945-4184","authenticated-orcid":false,"given":"Noam","family":"Zeilberger","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,2,5]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1803.10080v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1803.10080v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T13:37:04Z","timestamp":1743687424000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/4406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,5]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(1:9)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1803.10080v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1803.10080","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1803.10080","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,5]]},"article-number":"4406"}}