{"paper":{"title":"Hypercontractive Inequality for Pseudo-Boolean Functions of Bounded Fourier Width","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"cs.DM","authors_text":"Anders Yeo, Gregory Gutin","submitted_at":"2011-06-06T12:47:37Z","abstract_excerpt":"A function $f:\\ \\{-1,1\\}^n\\rightarrow \\mathbb{R}$ is called pseudo-Boolean. It is well-known that each pseudo-Boolean function $f$ can be written as $f(x)=\\sum_{I\\in {\\cal F}}\\hat{f}(I)\\chi_I(x),$ where ${\\cal F}\\subseteq \\{I:\\ I\\subseteq [n]\\}$, $[n]=\\{1,2,...,n\\}$, and $\\chi_I(x)=\\prod_{i\\in I}x_i$ and $\\hat{f}(I)$ are non-zero reals. The degree of $f$ is $\\max \\{|I|:\\ I\\in {\\cal F}\\}$ and the width of $f$ is the minimum integer $\\rho$ such that every $i\\in [n]$ appears in at most $\\rho$ sets in $\\cal F$. For $i\\in [n]$, let $\\mathbf{x}_i$ be a random variable taking values 1 or -1 uniformly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1049","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}