{"paper":{"title":"Non-trivial squares and Sidorenko's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amanda Redlich, Annie Raymond, Pranav Garg","submitted_at":"2022-06-21T00:45:01Z","abstract_excerpt":"Let $t(H;G)$ be the homomorphism density of a graph $H$ into a graph $G$. Sidorenko's conjecture states that for any bipartite graph $H$, $t(H;G)\\geq t(K_2;G)^{|E(H)|}$ for all graphs $G$. It is already known that such inequalities cannot be certified through the sums of squares method when $H$ is a so-called trivial square. In this paper, we investigate recent results about Sidorenko's conjecture and classify those involving trivial versus non-trivial squares. We then present some computational results. In particular, we categorize the bipartite graphs $H$ on at most 7 edges for which $t(H;G)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.10058","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/2206.10058/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"}