{"paper":{"title":"s-Inversion Sequences and P-Partitions of Type B","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alan J.X. Guo, Harry H.Y. Huang, Peter L. Guo, Thomas Y.H. Liu, William Y.C. Chen","submitted_at":"2013-10-20T09:34:00Z","abstract_excerpt":"Given a sequence $s=(s_1,s_2,\\ldots)$ of positive integers, the inversion sequences with respect to $s$, or $s$-inversion sequences, were introduced by Savage and Schuster in their study of lecture hall polytopes. A sequence $(e_1,e_2,\\ldots,e_n)$ of nonnegative integers is called an $s$-inversion sequence of length $n$ if $0\\leq e_i < s_i$ for $1\\leq i\\leq n$. Let I(n) be the set of $s$-inversion sequences of length $n$ for $s=(1,4,3,8,5,12,\\ldots)$, that is, $s_{2i}=4i$ and $s_{2i-1}=2i-1$ for $i\\geq1$, and let $P_n$ be the set of signed permutations on $\\{1^2,2^2,\\ldots,n^2\\}$. Savage and V"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5313","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":""},"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"}