{"paper":{"title":"On Delannoy paths without peaks and valleys","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heesung Shin, Seunghyun Seo","submitted_at":"2022-03-15T10:44:36Z","abstract_excerpt":"A lattice path is called \\emph{Delannoy} if its every step belongs to $\\left\\{N, E, D\\right\\}$, where $N=(0,1)$, $E=(1,0)$, and $D=(1,1)$ steps. \\emph{Peak}, \\emph{valley}, and \\emph{deep valley} mean $NE$, $EN$, and $EENN$ on the lattice path, respectively.\n  In this paper, we find a bijection between $\\mathcal{P}_{n,m}(NE, EN)$ and a specific subset of ${\\mathcal{P}_{n,m}}(D, EENN)$, where $\\mathcal{P}_{n,m}(NE, EN)$ is the set of Delannoy paths from the origin to the points $(n,m)$ without peaks and valleys and ${\\mathcal{P}_{n,m}}(D, EENN)$ is the set of Delannoy lattice paths from the ori"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.07770","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.07770/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}