{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,25]],"date-time":"2023-11-25T23:26:59Z","timestamp":1700954819301},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2017,3,6]],"date-time":"2017-03-06T00:00:00Z","timestamp":1488758400000},"content-version":"unspecified","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":[[2017,9]]},"DOI":"10.1007\/s00454-017-9880-0","type":"journal-article","created":{"date-parts":[[2017,3,6]],"date-time":"2017-03-06T21:05:27Z","timestamp":1488834327000},"page":"417-434","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Inclusion\u2013Exclusion Principles for Convex Hulls and the Euler Relation"],"prefix":"10.1007","volume":"58","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-8483-3373","authenticated-orcid":false,"given":"Zakhar","family":"Kabluchko","sequence":"first","affiliation":[]},{"given":"G\u00fcnter","family":"Last","sequence":"additional","affiliation":[]},{"given":"Dmitry","family":"Zaporozhets","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,3,6]]},"reference":[{"issue":"2","key":"9880_CR1","first-page":"39","volume":"43","author":"F Affentranger","year":"1988","unstructured":"Affentranger, F.: Generalization of a formula of C. Buchta about the convex hull of random points. Elem. Math. 43(2), 39\u201345 (1988)","journal-title":"Elem. Math."},{"issue":"5","key":"9880_CR2","first-page":"151","volume":"43","author":"F Affentranger","year":"1988","unstructured":"Affentranger, F.: Remarks on the note: \u201cGeneralization of a formula of C. Buchta about the convex hull of random points\u201d. Elem. Math. 43(5), 151\u2013152 (1988)","journal-title":"Elem. Math."},{"issue":"4","key":"9880_CR3","first-page":"104","volume":"44","author":"E Badertscher","year":"1989","unstructured":"Badertscher, E.: An explicit formula about the convex hull of random points. Elem. Math. 44(4), 104\u2013106 (1989)","journal-title":"Elem. Math."},{"issue":"1","key":"9880_CR4","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1007\/s00454-014-9649-7","volume":"53","author":"M Beermann","year":"2015","unstructured":"Beermann, M., Reitzner, M.: Beyond the Efron\u2013Buchta identities: distributional results for Poisson polytopes. Discrete Comput. Geom. 53(1), 226\u2013244 (2015)","journal-title":"Discrete Comput. Geom."},{"issue":"2","key":"9880_CR5","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/BF01490202","volume":"102","author":"C Buchta","year":"1986","unstructured":"Buchta, C.: On a conjecture of R.E. Miles about the convex hull of random points. Monatsh. Math. 102(2), 91\u2013102 (1986)","journal-title":"Monatsh. Math."},{"issue":"3","key":"9880_CR6","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/BF01061259","volume":"3","author":"C Buchta","year":"1990","unstructured":"Buchta, C.: Distribution-independent properties of the convex hull of random points. J. Theor. Probab. 3(3), 387\u2013393 (1990)","journal-title":"J. Theor. Probab."},{"issue":"1","key":"9880_CR7","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s00454-004-1109-3","volume":"33","author":"C Buchta","year":"2005","unstructured":"Buchta, C.: An identity relating moments of functionals of convex hulls. Discrete Comput. Geom. 33(1), 125\u2013142 (2005)","journal-title":"Discrete Comput. Geom."},{"issue":"3","key":"9880_CR8","doi-asserted-by":"crossref","first-page":"630","DOI":"10.1017\/S000186780000197X","volume":"39","author":"R Cowan","year":"2007","unstructured":"Cowan, R.: Identities linking volumes of convex hulls. Adv. Appl. Probab. 39(3), 630\u2013644 (2007)","journal-title":"Adv. Appl. Probab."},{"issue":"2","key":"9880_CR9","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s00454-008-9122-6","volume":"43","author":"R Cowan","year":"2010","unstructured":"Cowan, R.: Recurrence relationships for the mean number of faces and vertices for random convex hulls. Discrete Comput. Geom. 43(2), 209\u2013220 (2010)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"9880_CR10","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/BF01420497","volume":"198","author":"H Groemer","year":"1972","unstructured":"Groemer, H.: Eulersche Charakteristik Projektionen und Querma\u00dfintegrale. Math. Ann. 198(1), 23\u201356 (1972)","journal-title":"Math. Ann."},{"key":"9880_CR11","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-0019-9","volume-title":"Convex Polytopes","author":"B Gr\u00fcnbaum","year":"2003","unstructured":"Gr\u00fcnbaum, B.: Convex Polytopes. Graduate Texts in Mathematics, vol. 221, 2nd edn. Springer, New York (2003)","edition":"2"},{"key":"9880_CR12","unstructured":"Kabluchko, Z., Vysotsky, V., Zaporozhets, D.: Convex hulls of random walks, hyperplane arrangements, and Weyl chambers (2015). \n arXiv:1510.04073"},{"issue":"1","key":"9880_CR13","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF01564848","volume":"92","author":"W Nef","year":"1981","unstructured":"Nef, W.: Zur Einf\u00fchrung der Eulerschen Charakteristik. Monatsh. Math. 92(1), 41\u201346 (1981)","journal-title":"Monatsh. Math."},{"key":"9880_CR14","volume-title":"Convex Bodies: The Brunn\u2013Minkowski Theory. Encyclopedia of Mathematics and Its Applications","author":"R Schneider","year":"2014","unstructured":"Schneider, R.: Convex Bodies: The Brunn\u2013Minkowski Theory. Encyclopedia of Mathematics and Its Applications, vol. 151, 2nd edn. Cambridge University Press, Cambridge (2014)","edition":"2"},{"key":"9880_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-78859-1","volume-title":"Stochastic and Integral Geometry. Probability and Its Applications","author":"R Schneider","year":"2008","unstructured":"Schneider, R., Weil, W.: Stochastic and Integral Geometry. Probability and Its Applications. Springer, Berlin (2008)"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-017-9880-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-017-9880-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-017-9880-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,7,26]],"date-time":"2017-07-26T17:58:29Z","timestamp":1501091909000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-017-9880-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,6]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,9]]}},"alternative-id":["9880"],"URL":"https:\/\/doi.org\/10.1007\/s00454-017-9880-0","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,6]]}}}