{"paper":{"title":"Some Lucas-type congruences for q-trinomial coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Xiaoxia Wang, Yifan Chen","submitted_at":"2023-04-30T05:35:00Z","abstract_excerpt":"In this paper, we present several new $q$-congruences on the $q$-trinomial coefficients introduced by Andrews and Baxter. As a conclusion, we obtain the following congruence: \\begin{align*} \\bigg(\\!\\!\\binom{ap+b}{cp+d}\\!\\!\\bigg)\\equiv\\bigg(\\!\\!\\binom{a}{c}\\!\\!\\bigg)\\bigg(\\!\\!\\binom{b}{d}\\!\\!\\bigg)+\\bigg(\\!\\!\\binom{a}{c+1}\\!\\!\\bigg)\\bigg(\\!\\!\\binom{b}{d-p}\\!\\!\\bigg)\\pmod{p}, \\end{align*} where $a,b,c,d$ are integers subject to $a \\geq 0, 0 \\leq b,d \\leq p-1$, and $p$ is an odd prime.\n  Besides, we find that the method can also be used to reprove Pan's Lucas-type congruence for the $q$-Delannoy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.00396","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/2305.00396/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"}