{"paper":{"title":"On 021-Avoiding Ascent Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alvin Y. L. Dai, Bruce E. Sagan, Theodore Dokos, Tim Dwyer, William Y. C. Chen","submitted_at":"2012-06-13T15:47:01Z","abstract_excerpt":"Ascent sequences were introduced by Bousquet-M\\'{e}lou, Claesson, Dukes and Kitaev in their study of $(\\bf{2+2})$-free posets. An ascent sequence of length $n$ is a nonnegative integer sequence $x=x_{1}x_{2}... x_{n}$ such that $x_{1}=0$ and $x_{i}\\leq \\asc(x_{1}x_{2}...x_{i-1})+1$ for all $1<i\\leq n$, where $\\asc(x_{1}x_{2}...x_{i-1})$ is the number of ascents in the sequence $x_{1}x_{2}... x_{i-1}$. We let $\\cA_n$ stand for the set of such sequences and use $\\cA_n(p)$ for the subset of sequences avoiding a pattern $p$. Similarly, we let $S_{n}(\\tau)$ be the set of $\\tau$-avoiding permutation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2849","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":""},"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"}