{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T08:27:02Z","timestamp":1772267222296,"version":"3.50.1"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,4,2]],"date-time":"2015-04-02T00:00:00Z","timestamp":1427932800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2015,6]]},"DOI":"10.1007\/s00454-015-9685-y","type":"journal-article","created":{"date-parts":[[2015,4,1]],"date-time":"2015-04-01T18:49:13Z","timestamp":1427914153000},"page":"914-940","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Flip Invariance for Domino Tilings of Three-Dimensional Regions with Two Floors"],"prefix":"10.1007","volume":"53","author":[{"given":"Pedro H.","family":"Milet","sequence":"first","affiliation":[]},{"given":"Nicolau C.","family":"Saldanha","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,4,2]]},"reference":[{"issue":"2","key":"9685_CR1","first-page":"241","volume":"9","author":"O Bodini","year":"2007","unstructured":"Bodini, O., Jamet, D.: Tiling a pyramidal polycube with dominoes. Discrete Math. Theor. Comput. Sci. 9(2), 241\u2013254 (2007)","journal-title":"Discrete Math. Theor. Comput. Sci."},{"key":"9685_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1215\/S0012-7094-98-09401-7","volume":"94","author":"M Ciucu","year":"1998","unstructured":"Ciucu, M.: An improved upper bound for the three dimensional dimer problem. Duke Math. J. 94, 1\u201311 (1998)","journal-title":"Duke Math. J."},{"issue":"1","key":"9685_CR3","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1215\/S0012-7094-96-08506-3","volume":"85","author":"H Cohn","year":"1996","unstructured":"Cohn, H., Elkies, N., Propp, J., et al.: Local statistics for random domino tilings of the Aztec diamond. Duke Math. J. 85(1), 117\u2013166 (1996)","journal-title":"Duke Math. J."},{"issue":"2","key":"9685_CR4","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0097-3165(90)90057-4","volume":"53","author":"JH Conway","year":"1990","unstructured":"Conway, J.H., Lagarias, J.C.: Tiling with polyominoes and combinatorial group theory. J. Comb. Theory Ser. A 53(2), 183\u2013208 (1990)","journal-title":"J. Comb. Theory Ser. A"},{"issue":"3","key":"9685_CR5","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1023\/A:1022483817303","volume":"1","author":"N Elkies","year":"1992","unstructured":"Elkies, N., Kuperberg, G., Larsen, M., Propp, J.: Alternating-sign matrices and domino tilings (Part II). J. Algebr. Comb. 1(3), 219\u2013234 (1992)","journal-title":"J. Algebr. Comb."},{"issue":"3","key":"9685_CR6","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1016\/j.aam.2004.08.005","volume":"34","author":"S Friedland","year":"2005","unstructured":"Friedland, S., Peled, U.N.: Theory of computation of multidimensional entropy with an application to the monomer-dimer problem. Adv. Appl. Math. 34(3), 486\u2013522 (2005)","journal-title":"Adv. Appl. Math."},{"key":"9685_CR7","first-page":"125","volume-title":"Research Papers in Statistics: Festschrift for J. Neyman","author":"JM Hammersley","year":"1966","unstructured":"Hammersley, J.M.: Existence theorems and Monte Carlo methods for the monomer-dimer problem. In: David, F.N. (ed.) Research Papers in Statistics: Festschrift for J. Neyman, pp. 125\u2013146. Wiley, London (1966)"},{"key":"9685_CR8","unstructured":"Jockusch, W., Propp, J., Shor, P.: Random domino tilings and the arctic circle theorem. arXiv:math\/9801068 , (1995)"},{"issue":"12","key":"9685_CR9","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1016\/0031-8914(61)90063-5","volume":"27","author":"PW Kasteleyn","year":"1961","unstructured":"Kasteleyn, P.W.: The statistics of dimers on a lattice: I. The number of dimer arrangements on a quadratic lattice. Physica 27(12), 1209\u20131225 (1961)","journal-title":"Physica"},{"issue":"3","key":"9685_CR10","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1215\/S0012-7094-06-13134-4","volume":"131","author":"R Kenyon","year":"2006","unstructured":"Kenyon, R., Okounkov, A.: Planar dimers and Harnack curves. Duke Math. J. 131(3), 499\u2013524 (2006)","journal-title":"Duke Math. J."},{"issue":"3","key":"9685_CR11","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.4007\/annals.2006.163.1019","volume":"163","author":"R Kenyon","year":"2006","unstructured":"Kenyon, R., Okounkov, A.: Dimers and amoebae. Ann. Math. 163(3), 1019\u20131056 (2006)","journal-title":"Ann. Math."},{"key":"9685_CR12","first-page":"42","volume":"23","author":"J Linde","year":"2001","unstructured":"Linde, J., Moore, C., Nordahl, M.G.: An $$n$$ n -dimensional generalization of the rhombus tiling. Discrete Math. Theor. Comput. Sci. 23, 42 (2001)","journal-title":"Discrete Math. Theor. Comput. Sci."},{"key":"9685_CR13","unstructured":"Milet, P.H., Saldanha, N.C.: Domino tilings of three-dimensional regions: flips, trits and twists. arXiv:1410.7693 (2014)"},{"issue":"4","key":"9685_CR14","doi-asserted-by":"crossref","first-page":"P12","DOI":"10.37236\/2554","volume":"20","author":"I Pak","year":"2013","unstructured":"Pak, I., Yang, J.: The complexity of generalized domino tilings. Electron. J. Comb. 20(4), P12 (2013)","journal-title":"Electron. J. Comb."},{"key":"9685_CR15","unstructured":"Randall, D., Yngve, G.: Random three-dimensional tilings of Aztec octahedra and tetrahedra: an extension of domino tilings. In Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms, pp. 636\u2013645. Society for Industrial and Applied Mathematics, Philadelphia (2000)"},{"issue":"1","key":"9685_CR16","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/BF02570703","volume":"14","author":"NC Saldanha","year":"1995","unstructured":"Saldanha, N.C., Tomei, C., Casarin Jr, M.A., Romualdo, D.: Spaces of domino tilings. Discrete Comput. Geom. 14(1), 207\u2013233 (1995)","journal-title":"Discrete Comput. Geom."},{"issue":"8","key":"9685_CR17","doi-asserted-by":"crossref","first-page":"757","DOI":"10.2307\/2324578","volume":"97","author":"WP Thurston","year":"1990","unstructured":"Thurston, W.P.: Conway\u2019s tiling groups. Am. Math. Mon. 97(8), 757\u2013773 (1990)","journal-title":"Am. Math. Mon."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-015-9685-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-015-9685-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-015-9685-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T10:03:05Z","timestamp":1598868185000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-015-9685-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,2]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,6]]}},"alternative-id":["9685"],"URL":"https:\/\/doi.org\/10.1007\/s00454-015-9685-y","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,2]]}}}