{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,16]],"date-time":"2023-05-16T05:10:18Z","timestamp":1684213818073},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2008,1,31]],"date-time":"2008-01-31T00:00:00Z","timestamp":1201737600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Order"],"published-print":{"date-parts":[[2008,2]]},"DOI":"10.1007\/s11083-007-9075-z","type":"journal-article","created":{"date-parts":[[2008,1,30]],"date-time":"2008-01-30T11:41:25Z","timestamp":1201693285000},"page":"19-47","source":"Crossref","is-referenced-by-count":4,"title":["Orthogonal Surfaces and Their CP-Orders"],"prefix":"10.1007","volume":"25","author":[{"given":"Stefan","family":"Felsner","sequence":"first","affiliation":[]},{"given":"Sarah","family":"Kappes","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,1,31]]},"reference":[{"key":"9075_CR1","unstructured":"Adin, R.M., Roichman, Y.: On degrees in the Hasse diagram of the strong Bruhat order. S\u00e9m. Lothar. Combin. 53 (B53g), 12p (2006)"},{"key":"9075_CR2","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/S0012-365X(98)00309-4","volume":"201","author":"G. Agnarsson","year":"1999","unstructured":"Agnarsson, G., Felsner, S., Trotter, W.T.: The maximum number of edges in a graph of bounded dimension, with applications to ring theory. Discrete Math. 201, 5\u201319 (1999)","journal-title":"Discrete Math."},{"key":"9075_CR3","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/S0195-6698(85)80028-7","volume":"6","author":"N. Alon","year":"1985","unstructured":"Alon, N., F\u00fcredi, Z., Katchalski, M.: Separating pairs of points. Europ. J. Comb. 6, 205\u2013210 (1985)","journal-title":"Europ. J. Comb."},{"key":"9075_CR4","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/BF02483890","volume":"12","author":"L. Babai","year":"1981","unstructured":"Babai, L., Duffus, D.: Dimension and automorphism groups of lattices. Algebra Univers. 12, 279\u2013289 (1981)","journal-title":"Algebra Univers."},{"key":"9075_CR5","doi-asserted-by":"crossref","first-page":"369","DOI":"10.4171\/dm\/214","volume":"11","author":"I. B\u00e1r\u00e1ny","year":"2006","unstructured":"B\u00e1r\u00e1ny, I., Rote, G.: Strictly convex drawings of planar graphs. Doc. Math. 11, 369\u2013391 (2006)","journal-title":"Doc. Math."},{"key":"9075_CR6","doi-asserted-by":"crossref","first-page":"31","DOI":"10.4310\/MRL.1998.v5.n1.a3","volume":"5","author":"D. Bayer","year":"1998","unstructured":"Bayer, D., Peeva, I., Sturmfels, B.: Monomial resolutions. Math. Res. Lett. 5, 31\u201346 (1998)","journal-title":"Math. Res. Lett."},{"key":"9075_CR7","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s00453-006-0177-6","volume":"47","author":"N. Bonichon","year":"2007","unstructured":"Bonichon, N., Felsner, S., Mosbah, M.: Convex drawings of 3-connected planar graphs. Algorithmica 47, 399\u2013420 (2007)","journal-title":"Algorithmica"},{"key":"9075_CR8","doi-asserted-by":"crossref","unstructured":"Bonichon, N., Le Sa\u00ebc, B., Mosbah, M.: Optimal area algorithm for planar polyline drawings. In: Proceedings WG\u201902, Lecture Notes Comput. Sci., vol. 2573, pp. 35\u201346. Springer-Verlag (2002)","DOI":"10.1007\/3-540-36379-3_4"},{"key":"9075_CR9","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1137\/0406018","volume":"6","author":"G. Brightwell","year":"1993","unstructured":"Brightwell, G., Trotter, W.T.: The order dimension of convex polytopes. SIAM J. Discrete Math. 6, 230\u2013245 (1993)","journal-title":"SIAM J. Discrete Math."},{"key":"9075_CR10","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/S0012-365X(00)00201-6","volume":"229","author":"H. Fraysseix de","year":"2001","unstructured":"de Fraysseix, H., de Mendez, P.O.: On topological aspects of orientation. Discrete Math. 229, 57\u201372 (2001)","journal-title":"Discrete Math."},{"key":"9075_CR11","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1007\/PL00009264","volume":"23","author":"G. Di Battista","year":"1999","unstructured":"Di Battista, G., Tamassia, R., Vismara, L.: Output-sensitive reporting of disjoint paths. Algorithmica 23, 302\u2013340 (1999)","journal-title":"Algorithmica"},{"key":"9075_CR12","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1023\/A:1010604726900","volume":"18","author":"S. Felsner","year":"2001","unstructured":"Felsner, S.: Convex drawings of planar graphs and the order dimension of 3-polytopes. Order 18, 19\u201337 (2001)","journal-title":"Order"},{"key":"9075_CR13","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1023\/B:ORDE.0000009251.68514.8b","volume":"20","author":"S. Felsner","year":"2003","unstructured":"Felsner, S.: Geodesic embeddings of planar graphs. Order 20, 135\u2013150 (2003)","journal-title":"Order"},{"key":"9075_CR14","doi-asserted-by":"crossref","unstructured":"Felsner, S.: Geometric Graphs and Arrangements. Vieweg Verlag (2004)","DOI":"10.1007\/978-3-322-80303-0"},{"key":"9075_CR15","doi-asserted-by":"crossref","unstructured":"Felsner, S.: Lattice structures from planar graphs. Electron. J. Combin. 11, 24p (2004)","DOI":"10.37236\/1768"},{"key":"9075_CR16","unstructured":"Felsner, S.: Empty rectangles and graph dimension. (2006) http:\/\/arxiv.org\/abs\/math.CO\/0601767"},{"key":"9075_CR17","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1002\/jgt.20081","volume":"49","author":"S. Felsner","year":"2005","unstructured":"Felsner, S., Trotter, W.T.: Posets and planar graphs. J. Graph Theory 49, 262\u2013272 (2005)","journal-title":"J. Graph Theory"},{"key":"9075_CR18","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/978-3-540-70904-6_40","volume-title":"Proceedings Graph Drawing","author":"S. Felsner","year":"2007","unstructured":"Felsner, S., Zickfeld, F.: Schnyder woods and orthogonal surfaces. In Proceedings Graph Drawing, pp. 417\u2013429, Karlsruhe, Germany (2007)"},{"key":"9075_CR19","unstructured":"Fusy, E., Poulalhon, D., Schaeffer, G.: Dissection and trees, with applications to optimal mesh encoding and random sampling. In: Proc. 16. ACM-SIAM Sympos. Discrete Algorithms, ACACM Transactions on Algorithms, pp. 690\u2013699 (2005)"},{"key":"9075_CR20","doi-asserted-by":"crossref","unstructured":"Gr\u00fcnbaum, B.: Convex polytopes. Graduate Texts in Mathematics, vol.\u00a0221. Springer-Verlag (2003)","DOI":"10.1007\/978-1-4613-0019-9"},{"key":"9075_CR21","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/S0012-365X(98)00315-X","volume":"201","author":"S. Ho\u015ften","year":"1999","unstructured":"Ho\u015ften, S., Morris, W.D.: The order dimension of the complete graph. Discrete Math. 201, 133\u2013139 (1999)","journal-title":"Discrete Math."},{"key":"9075_CR22","unstructured":"Kappes, S.: Orthogonal surfaces: A combinatorial approach. PhD thesis. (2006). http:\/\/www.math.tu-berlin.de\/diskremath\/sarahs_diss.pdf"},{"key":"9075_CR23","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1137\/S0895480103420744","volume":"18","author":"C. Lin","year":"2004","unstructured":"Lin, C., Lu, H., Sun, I.-F.: Improved compact visibility representation of planar graphs via Schnyder\u2019s realizer. SIAM J. Discrete Math. 18, 19\u201329 (2004)","journal-title":"SIAM J. Discrete Math."},{"key":"9075_CR24","doi-asserted-by":"crossref","first-page":"43","DOI":"10.4171\/dm\/117","volume":"7","author":"E. Miller","year":"2002","unstructured":"Miller, E.: Planar graphs as minimal resolutions of trivariate monomial ideals. Documenta Math. 7, 43\u201390 (2002)","journal-title":"Documenta Math."},{"key":"9075_CR25","unstructured":"Miller, E., Sturmfels, B.: Combinatorial Commutative Algebra. Graduate Texts in Mathematics, Springer-Verlag (2004)"},{"key":"9075_CR26","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1007\/s00453-006-0114-8","volume":"46","author":"D. Poulalhon","year":"2006","unstructured":"Poulalhon, D., Schaeffer, G.: Optimal coding and sampling of triangulations. Algorithmica 46, 505\u2013527 (2006)","journal-title":"Algorithmica"},{"key":"9075_CR27","unstructured":"Scarf, H.: The Computation of Economic Equilibria. Cowles Foundation Monograph, vol.\u00a024. Yale University Press (1973)"},{"key":"9075_CR28","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/BF00353652","volume":"5","author":"W. Schnyder","year":"1989","unstructured":"Schnyder, W.: Planar graphs and poset dimension. Order 5, 323\u2013343 (1989)","journal-title":"Order"},{"key":"9075_CR29","unstructured":"Schnyder, W.: Embedding planar graphs on the grid. In: Proc. 1st ACM-SIAM Sympos. Discrete Algorithms, pp.\u00a0138\u2013148 (1990)"},{"key":"9075_CR30","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF01896428","volume":"22","author":"J. Spencer","year":"1972","unstructured":"Spencer, J.: Minimal scrambling sets of simple orders. Acta Math. Acad. Sci. Hungar. 22, 349\u2013353 (1972)","journal-title":"Acta Math. Acad. Sci. Hungar."},{"key":"9075_CR31","doi-asserted-by":"crossref","unstructured":"Trotter, W.T.: Combinatorics and Partially Ordered Sets: Dimension Theory. Johns Hopkins Series in the Mathematical Sciences. The Johns Hopkins University Press (1992)","DOI":"10.56021\/9780801844256"},{"key":"9075_CR32","doi-asserted-by":"crossref","unstructured":"Ziegler, G.M.: Lectures on Polytopes. Graduate Texts in Mathematics, vol.\u00a0152 Springer-Verlag (1994)","DOI":"10.1007\/978-1-4613-8431-1"}],"container-title":["Order"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-007-9075-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11083-007-9075-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-007-9075-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,16]],"date-time":"2023-05-16T04:54:54Z","timestamp":1684212894000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11083-007-9075-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1,31]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,2]]}},"alternative-id":["9075"],"URL":"https:\/\/doi.org\/10.1007\/s11083-007-9075-z","relation":{},"ISSN":["0167-8094","1572-9273"],"issn-type":[{"value":"0167-8094","type":"print"},{"value":"1572-9273","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1,31]]}}}