{"paper":{"title":"Lattice paths inside a table: Rows and columns linear combinations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Mohammad Farrokhi Derakhshandeh Ghouchan","submitted_at":"2019-10-22T09:02:05Z","abstract_excerpt":"A lattice path inside the $m\\times n$ table $T$ is a sequence $\\nu_1,\\ldots,\\nu_k$ of cells such that $\\nu_{j+1}-\\nu_j\\in\\{(1,-1),(1,0),(1,1)\\}$ for all $j=1,\\ldots,k-1$. The number of lattice paths in $T$ from the first column to the $(x,y)$-cell is written into that cell. We present a precise description of the minimal linear recurrences among rows, columns, and columns sums. As a result, we obtain several formulas for the number of all lattice paths from the first column to the last column of $T$, that is, the $n^{th}$ column sum. Our methods are based on three classes of operators, which w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.09844","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.09844/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"}