{"paper":{"title":"Cliques of orders three and four in the Paley-type graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Anwita Bhowmik, Rupam Barman","submitted_at":"2023-01-17T17:14:00Z","abstract_excerpt":"Let $n=2^s p_{1}^{\\alpha_{1}}\\cdots p_{k}^{\\alpha_{k}}$, where $s=0$ or $1$, $\\alpha_i\\geq 1$, and the distinct primes $p_i$ satisfy $p_i\\equiv 1\\pmod{4}$ for all $i=1, \\ldots, k$. Let $\\mathbb{Z}_n^\\ast$ denote the group of units in the commutative ring $\\mathbb{Z}_n$. Recently, we defined a Paley-type graph $G_n$ of order $n$ as the graph whose vertex set is $\\mathbb{Z}_n$ and $xy$ is an edge if $x-y\\equiv a^2\\pmod n$ for some $a\\in\\mathbb{Z}_n^\\ast$. The Paley-type graph $G_n$ resembles the classical Paley graph in a number of ways, and adds to the list of generalizations of the Paley graph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.07021","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/2301.07021/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"}