{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T18:07:19Z","timestamp":1769969239299,"version":"3.49.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,1,19]],"date-time":"2018-01-19T00:00:00Z","timestamp":1516320000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"ECOS Nord project M13M01"},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["1452\/15"],"award-info":[{"award-number":["1452\/15"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["678765"],"award-info":[{"award-number":["678765"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2018,10]]},"DOI":"10.1007\/s00454-018-9965-4","type":"journal-article","created":{"date-parts":[[2018,1,19]],"date-time":"2018-01-19T15:11:25Z","timestamp":1516374685000},"page":"698-719","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["On Lattice Path Matroid Polytopes: Integer Points and Ehrhart Polynomial"],"prefix":"10.1007","volume":"60","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8151-2184","authenticated-orcid":false,"given":"Kolja","family":"Knauer","sequence":"first","affiliation":[]},{"given":"Leonardo","family":"Mart\u00ednez-Sandoval","sequence":"additional","affiliation":[]},{"given":"Jorge Luis","family":"Ram\u00edrez Alfons\u00edn","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,1,19]]},"reference":[{"key":"9965_CR1","unstructured":"An, S., Jung, J., Kim, S.: Facial structures of lattice path matroid polytopes. arXiv:1701.00362 (2017)"},{"key":"9965_CR2","unstructured":"Bidkhori, H.: Lattice path matroid polytopes. arXiv:1212.5705 (2012)"},{"issue":"3","key":"9965_CR3","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1215\/S0012-7094-37-00334-X","volume":"3","author":"G Birkhoff","year":"1937","unstructured":"Birkhoff, G.: Rings of sets. Duke Math. J. 3(3), 443\u2013454 (1937)","journal-title":"Duke Math. J."},{"issue":"6","key":"9965_CR4","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1016\/j.jctb.2010.05.001","volume":"100","author":"JE Bonin","year":"2010","unstructured":"Bonin, J.E.: Lattice path matroids: the excluded minors. J. Combin. Theory Ser. B 100(6), 585\u2013599 (2010)","journal-title":"J. Combin. Theory Ser. B"},{"issue":"1","key":"9965_CR5","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/S0097-3165(03)00122-5","volume":"104","author":"J Bonin","year":"2003","unstructured":"Bonin, J., de Mier, A., Noy, M.: Lattice path matroids: enumerative aspects and Tutte polynomials. J. Combin. Theory Ser. A 104(1), 63\u201394 (2003)","journal-title":"J. Combin. Theory Ser. A"},{"issue":"2","key":"9965_CR6","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1017\/S0963548306007942","volume":"16","author":"JE Bonin","year":"2007","unstructured":"Bonin, J.E., Gim\u00e9nez, O.: Multi-path matroids. Combin. Probab. Comput. 16(2), 193\u2013217 (2007)","journal-title":"Combin. Probab. Comput."},{"key":"9965_CR7","series-title":"Discrete Mathematics and Its Applications","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1201\/b18255-10","volume-title":"Handbook of Enumerative Combinatorics","author":"P Br\u00e4nd\u00e9n","year":"2015","unstructured":"Br\u00e4nd\u00e9n, P.: Unimodality, log-concavity, real-rootedness and beyond. In: Bona, M. (ed.) Handbook of Enumerative Combinatorics. Discrete Mathematics and Its Applications, pp. 437\u2013483. CRC Press, Boca Raton (2015)"},{"issue":"1","key":"9965_CR8","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1016\/j.aam.2010.04.005","volume":"47","author":"V Chatelain","year":"2011","unstructured":"Chatelain, V., Ram\u00edrez Alfons\u00edn, J.L.: Matroid base polytope decomposition. Adv. Appl. Math. 47(1), 158\u2013172 (2011)","journal-title":"Adv. Appl. Math."},{"key":"9965_CR9","unstructured":"Cohen, E., Tetali, P., Yeliussizov, D.: Lattice path matroids: negative correlation and fast mixing. arXiv:1505.06710 (2015)"},{"key":"9965_CR10","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809088","volume-title":"Introduction to Lattices and Order","author":"BA Davey","year":"2002","unstructured":"Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, New York (2002)","edition":"2"},{"issue":"4","key":"9965_CR11","doi-asserted-by":"publisher","first-page":"670","DOI":"10.1007\/s00454-008-9080-z","volume":"42","author":"JA Loera De","year":"2009","unstructured":"De Loera, J.A., Haws, D.C., K\u00f6ppe, M.: Ehrhart polynomials of matroid polytopes and polymatroids. Discrete Comput. Geom. 42(4), 670\u2013702 (2009)","journal-title":"Discrete Comput. Geom."},{"issue":"4","key":"9965_CR12","doi-asserted-by":"publisher","first-page":"1916","DOI":"10.1137\/130944242","volume":"29","author":"E Delucchi","year":"2015","unstructured":"Delucchi, E., Dlugosch, M.: Bergman complexes of lattice path matroids. SIAM J. Discrete Math. 29(4), 1916\u20131930 (2015)","journal-title":"SIAM J. Discrete Math."},{"issue":"1","key":"9965_CR13","doi-asserted-by":"publisher","first-page":"161","DOI":"10.2307\/1969503","volume":"51","author":"RP Dilworth","year":"1950","unstructured":"Dilworth, R.P.: A decomposition theorem for partially ordered sets. Ann. Math. (2) 51(1), 161\u2013166 (1950)","journal-title":"Ann. Math. (2)"},{"key":"9965_CR14","first-page":"616","volume":"254","author":"E Ehrhart","year":"1962","unstructured":"Ehrhart, E.: Sur les poly\u00e8dres rationnels homoth\u00e9tiques \u00e0 $$n$$ n dimensions. C. R. Acad. Sci. 254, 616\u2013618 (1962)","journal-title":"C. R. Acad. Sci."},{"issue":"4","key":"9965_CR15","first-page":"437","volume":"62","author":"EM Feichtner","year":"2005","unstructured":"Feichtner, E.M., Sturmfels, B.: Matroid polytopes, nested sets and Bergman fans. Port. Math. (N.S.) 62(4), 437\u2013468 (2005)","journal-title":"Port. Math. (N.S.)"},{"issue":"1","key":"9965_CR16","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1016\/j.ejc.2010.07.011","volume":"32","author":"S Felsner","year":"2011","unstructured":"Felsner, S., Knauer, K.: Distributive lattices, polyhedra, and generalized flows. Eur. J. Combin. 32(1), 45\u201359 (2011)","journal-title":"Eur. J. Combin."},{"issue":"4","key":"9965_CR17","doi-asserted-by":"publisher","first-page":"1141","DOI":"10.1081\/AGB-200053828","volume":"33","author":"M Katzman","year":"2005","unstructured":"Katzman, M.: The Hilbert series of Veronese type. Commun. Algebra 33(4), 1141\u20131146 (2005)","journal-title":"Commun. Algebra"},{"key":"9965_CR18","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/j.aam.2016.11.008","volume":"94","author":"K Knauer","year":"2018","unstructured":"Knauer, K., Mart\u00ednez-Sandoval, L., Alfons\u00edn, J.L.: A Tutte polynomial inequality for lattice path matroids. Adv. Appl. Math. 94, 23\u201338 (2018)","journal-title":"Adv. Appl. Math."},{"key":"9965_CR19","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.tcs.2015.07.042","volume":"598","author":"J Morton","year":"2015","unstructured":"Morton, J., Turner, J.: Computing the Tutte polynomial of lattice path matroids using determinantal circuits. Theor. Comput. Sci. 598, 150\u2013156 (2015)","journal-title":"Theor. Comput. Sci."},{"issue":"3","key":"9965_CR20","first-page":"113","volume":"3","author":"J Neggers","year":"1978","unstructured":"Neggers, J.: Representations of finite partially ordered sets. J. Combin. Inf. Syst. Sci. 3(3), 113\u2013133 (1978)","journal-title":"J. Combin. Inf. Syst. Sci."},{"key":"9965_CR21","volume-title":"Matroid Theory. Oxford Graduate Texts in Mathematics","author":"J Oxley","year":"2011","unstructured":"Oxley, J.: Matroid Theory. Oxford Graduate Texts in Mathematics, vol. 21, 2nd edn. Oxford University Press, Oxford (2011)","edition":"2"},{"issue":"2","key":"9965_CR22","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.jcta.2004.09.003","volume":"109","author":"V Reiner","year":"2005","unstructured":"Reiner, V., Welker, V.: On the Charney\u2013Davis and Neggers\u2013Stanley conjectures. J. Combin. Theory Ser. A 109(2), 247\u2013280 (2005)","journal-title":"J. Combin. Theory Ser. A"},{"issue":"1","key":"9965_CR23","doi-asserted-by":"crossref","first-page":"Note 3","DOI":"10.37236\/452","volume":"17","author":"J Schweig","year":"2010","unstructured":"Schweig, J.: On the $$h$$ h -vector of a lattice path matroid. Electron. J. Combin. 17(1), Note 3 (2010)","journal-title":"Electron. J. Combin."},{"issue":"11","key":"9965_CR24","doi-asserted-by":"publisher","first-page":"2660","DOI":"10.1016\/j.jpaa.2011.03.010","volume":"215","author":"J Schweig","year":"2011","unstructured":"Schweig, J.: Toric ideals of lattice path matroids and polymatroids. J. Pure Appl. Algebra 215(11), 2660\u20132665 (2011)","journal-title":"J. Pure Appl. Algebra"},{"issue":"1","key":"9965_CR25","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/0097-3165(84)90075-X","volume":"36","author":"R Simion","year":"1984","unstructured":"Simion, R.: A multi-indexed Sturm sequence of polynomials and unimodality of certain combinatorial sequences. J. Combin. Theory Ser. A 36(1), 15\u201322 (1984)","journal-title":"J. Combin. Theory Ser. A"},{"key":"9965_CR26","unstructured":"Stanley, R.P.: A chromatic-like polynomial for ordered sets. In: Proceedings of the 2nd Chapel Hill Conference on Combinatorial Mathematics and its Applications, pp. 421\u2013427. University of North Carolina, Chapel Hill (1970)"},{"issue":"1","key":"9965_CR27","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/BF02187680","volume":"1","author":"RP Stanley","year":"1986","unstructured":"Stanley, R.P.: Two poset polytopes. Discrete Comput. Geom. 1(1), 9\u201323 (1986)","journal-title":"Discrete Comput. Geom."},{"issue":"2","key":"9965_CR28","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1090\/S0002-9947-97-01804-7","volume":"349","author":"JR Stembridge","year":"1997","unstructured":"Stembridge, J.R.: Enriched $$P$$ P -partitions. Trans. Am. Math. Soc. 349(2), 763\u2013788 (1997)","journal-title":"Trans. Am. Math. Soc."},{"issue":"3","key":"9965_CR29","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1090\/S0002-9947-06-04271-1","volume":"359","author":"JR Stembridge","year":"2007","unstructured":"Stembridge, J.R.: Counterexamples to the poset conjectures of Neggers, Stanley, and Stembridge. Trans. Am. Math. Soc. 359(3), 1115\u20131128 (2007)","journal-title":"Trans. Am. Math. Soc."},{"issue":"2","key":"9965_CR30","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1016\/0022-247X(92)90261-B","volume":"163","author":"DG Wagner","year":"1992","unstructured":"Wagner, D.G.: Total positivity of Hadamard products. J. Math. Anal. Appl. 163(2), 459\u2013483 (1992)","journal-title":"J. Math. Anal. Appl."},{"key":"9965_CR31","volume-title":"Matroid Theory. L. M. S. Monographs,","author":"DJA Welsh","year":"1976","unstructured":"Welsh, D.J.A.: Matroid Theory. L. M. S. Monographs, vol. 8. Academic Press, London (1976)"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-018-9965-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-018-9965-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-018-9965-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,25]],"date-time":"2020-10-25T21:56:43Z","timestamp":1603663003000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-018-9965-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,19]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,10]]}},"alternative-id":["9965"],"URL":"https:\/\/doi.org\/10.1007\/s00454-018-9965-4","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,19]]},"assertion":[{"value":"19 January 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 December 2017","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 January 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}