{"paper":{"title":"New results on torus cube packings and tilings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.MG","authors_text":"Mathieu Dutour Sikiri\\'c, Yoshiaki Itoh","submitted_at":"2014-10-03T12:51:11Z","abstract_excerpt":"We consider sequential random packing of integral translate of cubes $[0,N]^n$ into the torus $Z^n / 2NZ^n$. Two special cases are of special interest:\n  (i) The case $N=2$ which corresponds to a discrete case of tilings (considered in \\cite{cubetiling,book})\n  (ii) The case $N=\\infty$ corresponds to a case of continuous tilings (considered in \\cite{combincubepack,book})\n  Both cases correspond to some special combinatorial structure and we describe here new developments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0839","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"}