{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T23:17:22Z","timestamp":1775258242077,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,10,26]],"date-time":"2018-10-26T00:00:00Z","timestamp":1540512000000},"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":["Order"],"published-print":{"date-parts":[[2019,11]]},"DOI":"10.1007\/s11083-018-9473-4","type":"journal-article","created":{"date-parts":[[2018,10,26]],"date-time":"2018-10-26T02:39:58Z","timestamp":1540521598000},"page":"399-422","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["d-Complete Posets: Local Structural Axioms, Properties, and Equivalent Definitions"],"prefix":"10.1007","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3421-4624","authenticated-orcid":false,"given":"Robert A.","family":"Proctor","sequence":"first","affiliation":[]},{"given":"Lindsey M.","family":"Scoppetta","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,10,26]]},"reference":[{"key":"9473_CR1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1515\/crelle-2014-0051","volume":"719","author":"A Buch","year":"2016","unstructured":"Buch, A., Samuel, M.: K-theory of minuscule varieties. J. Reine Angew. Math. 719, 133\u2013171 (2016)","journal-title":"J. Reine Angew. Math."},{"key":"9473_CR2","unstructured":"Carrell, J.: Vector fields, flag varieties, and Schubert calculus. In: Proceedings of the Hyderabad Conference on Algebraic Groups, pp. 23\u201357. Manoj Prakashan Madras Ramanan, S. (ed.) (1991)"},{"key":"9473_CR3","doi-asserted-by":"crossref","first-page":"17","DOI":"10.5802\/jolt.660","volume":"22","author":"P-E Chaput","year":"2012","unstructured":"Chaput, P.-E., Perrin, N.: Towards a Littlewood-Richardson rule for Kac-Moody homogeneous spaces. J. Lie Theory 22, 17\u201380 (2012)","journal-title":"J. Lie Theory"},{"key":"9473_CR4","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139005135","volume-title":"Finite Ordered Sets: Concepts, Results and Uses","author":"N Caspard","year":"2012","unstructured":"Caspard, N., Leclerc, B., Monjardet, B.: Finite Ordered Sets: Concepts, Results and Uses. Cambridge University Press, New York (2012)"},{"key":"9473_CR5","unstructured":"Gann, C., Proctor, R. Chapel Hill Poset Atlas. www.unc.edu\/\u223clowrap\/Posets (2005)"},{"key":"9473_CR6","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139207003","volume-title":"Combinatorics of Minuscule Representations","author":"RM Green","year":"2013","unstructured":"Green, R.M.: Combinatorics of Minuscule Representations. Cambridge University Press, Cambridge (2013)"},{"key":"9473_CR7","unstructured":"Ilango, R., Pechenik, O., Zlatin, M.: Unique rectification in d-complete posets: towards the K-theory of Kac-Moody flag varieties. arXiv: 1805.02287"},{"key":"9473_CR8","first-page":"47","volume":"1913","author":"M Ishikawa","year":"2014","unstructured":"Ishikawa, M.: (q,t)-hook formula for birds. RIMS K\u00f4ky\u00fbroku 1913, 47\u201366 (2014)","journal-title":"RIMS K\u00f4ky\u00fbroku"},{"key":"9473_CR9","first-page":"101","volume":"1262","author":"M Ishikawa","year":"2002","unstructured":"Ishikawa, M., Tagawa, H.: Determinants and Pfaffians associated with d-complete posets. RIMS K\u00f4ky\u00fbroku 1262, 101\u2013136 (2002)","journal-title":"RIMS K\u00f4ky\u00fbroku"},{"key":"9473_CR10","first-page":"67","volume":"1913","author":"M Ishikawa","year":"2014","unstructured":"Ishikawa, M., Tagawa, H.: Leaf posets and multivariate hook length property. RIMS K\u00f4ky\u00fbroku 1913, 67\u201380 (2014)","journal-title":"RIMS K\u00f4ky\u00fbroku"},{"key":"9473_CR11","first-page":"95","volume":"1190","author":"N Kawanaka","year":"2001","unstructured":"Kawanaka, N.: Sato-welter game and Kac-Moody Lie algebras. RIMS K\u00f4ky\u00fbroku 1190, 95\u2013106 (2001)","journal-title":"RIMS K\u00f4ky\u00fbroku"},{"key":"9473_CR12","first-page":"73","volume":"28","author":"N Kawanaka","year":"2015","unstructured":"Kawanaka, N.: Games and algorithms with hook structure. Sugaku Expositions 28, 73\u201393 (2015)","journal-title":"Sugaku Expositions"},{"key":"9473_CR13","unstructured":"Kim, J.S., Yoo, M.: Hook length property of d-complete posets via q-integrals, arXiv: 1708.09109"},{"key":"9473_CR14","doi-asserted-by":"publisher","first-page":"1293","DOI":"10.4171\/JEMS\/230","volume":"12","author":"A Kleshchev","year":"2010","unstructured":"Kleshchev, A., Ram, A.: Homogeneous representations of Khovanov-Lauda algebras. J. Eur. Math. Soc. 12, 1293\u20131306 (2010)","journal-title":"J. Eur. Math. Soc."},{"key":"9473_CR15","doi-asserted-by":"crossref","unstructured":"Konvalinka, M.: The weighted hook length formula III: Shifted tableaux, vol. 18 (2011)","DOI":"10.1016\/j.ejc.2011.01.005"},{"key":"9473_CR16","doi-asserted-by":"crossref","unstructured":"Lax, D.: Order Filter Model for Minuscule Pl\u00fccker Relations, to Appear in 28th Inter. Conf. on Formal Power Series and Algebraic Combins (FPSAC 2016). Discrete Math. Theor. Comput. Sci. Proc","DOI":"10.46298\/dmtcs.6404"},{"key":"9473_CR17","first-page":"1085","volume":"45","author":"K Nakada","year":"2008","unstructured":"Nakada, K.: Colored hook formula for a generalized Young diagram. Osaka J. Math. 45, 1085\u20131120 (2008)","journal-title":"Osaka J. Math."},{"key":"9473_CR18","doi-asserted-by":"crossref","unstructured":"Nakada, K.: Q-Hook formula of Gansner type for a generalized Young diagram. In: 21st Inter. Conf. on Formal Power Series and Algebraic Combins. (FPSAC 2009), vol. 685\u2013696. Discrete Math. Theor. Comput. Sci. Proc., AK, Assoc. Discrete Math. Theor. Comput. Sci., Nancy (2009)","DOI":"10.46298\/dmtcs.2684"},{"key":"9473_CR19","first-page":"106","volume":"1913","author":"K Nakada","year":"2014","unstructured":"Nakada, K.: Generalization of Young diagrams and hook formula. RIMS K\u00f4ky\u00fbroku 1913, 106\u2013111 (2014)","journal-title":"RIMS K\u00f4ky\u00fbroku"},{"key":"9473_CR20","doi-asserted-by":"crossref","unstructured":"Nakada, K., Okamura, S.: An algorithm which generates linear extensions for a generalized Young diagram with uniform probability. In: 22nd Inter. Conf. on Formal Power Series and Algebraic Combins (FPSAC 2010), vol. 933\u2013939. Discrete Math. Theor. Comput. Sci. Proc., AN, Assoc. Discrete Math. Theor. Comput. Sci., Nancy (2010)","DOI":"10.46298\/dmtcs.2843"},{"key":"9473_CR21","unstructured":"Naruse, H., Okada, S.: Skew hook formula for d-complete posets, arXiv: 1802.09748"},{"key":"9473_CR22","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/s10801-010-0221-0","volume":"32","author":"S Okada","year":"2010","unstructured":"Okada, S.: (q,t)-Deformations of multivariate hook product formulae. J. Algebr. Combinatorics 32, 399\u2013416 (2010)","journal-title":"J. Algebr. Combinatorics"},{"key":"9473_CR23","unstructured":"Okamura, S.: An Algorithm Which Generates, Uniform Randomly, Standard Young Tableaux in a Generalized Sense (Japanese). Master\u2019s thesis, Osaka University (2003)"},{"key":"9473_CR24","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1016\/S0195-6698(84)80037-2","volume":"5","author":"R Proctor","year":"1984","unstructured":"Proctor, R.: Bruhat lattices, plane partition generating functions, and minuscule representations. Europ. J. Combinatorics 5, 331\u2013350 (1984)","journal-title":"Europ. J. Combinatorics"},{"key":"9473_CR25","unstructured":"Proctor, R.: Poset partitions and minuscule representations: External construction of Lie representations. Part I, unpublished manuscript (1993)"},{"key":"9473_CR26","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1023\/A:1018615115006","volume":"9","author":"R Proctor","year":"1999","unstructured":"Proctor, R.: Dynkin diagram classification of \u03bb-minuscule Bruhat lattices and of d-complete posets. J. Algebraic Combinatorics 9, 61\u201394 (1999)","journal-title":"J. Algebraic Combinatorics"},{"key":"9473_CR27","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1006\/jabr.1998.7648","volume":"213","author":"R Proctor","year":"1999","unstructured":"Proctor, R.: Minuscule elements of Weyl groups, the numbers game, and d-complete posets. J. Algebra 213, 272\u2013303 (1999)","journal-title":"J. Algebra"},{"key":"9473_CR28","unstructured":"Proctor, R.: d-complete posets generalize Young diagrams for the jeu de taquin property. ArXiv: 0905.3716"},{"key":"9473_CR29","first-page":"120","volume":"1913","author":"R Proctor","year":"2014","unstructured":"Proctor, R.: d-complete posets generalize Young diagrams for the hook product formula: Partial presentation of proof. RIMS K\u00f4ky\u00fbroku 1913, 120\u2013140 (2014)","journal-title":"RIMS K\u00f4ky\u00fbroku"},{"key":"9473_CR30","unstructured":"Riegler, L., Neumann, C.: Playing jeu de taquin on d-complete posets. s\u00e9m. Loth. Combin. 74, Art B74d (2016)"},{"key":"9473_CR31","first-page":"1","volume":"119","author":"R Stanley","year":"1972","unstructured":"Stanley, R.: Ordered structures and partitions. Mem. Amer. Math. Soc. 119, 1\u2013104 (1972)","journal-title":"Mem. Amer. Math. Soc."},{"key":"9473_CR32","unstructured":"Stanley, R.: Enumerative Combinatorics, 2nd edn., vol. I. Cambridge University Press, New York (2012)"},{"key":"9473_CR33","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1006\/jabr.2000.8488","volume":"235","author":"J Stembridge","year":"2001","unstructured":"Stembridge, J.: Minuscule elements of Weyl groups. J. Algebra 235, 722\u2013743 (2001)","journal-title":"J. Algebra"},{"key":"9473_CR34","unstructured":"Strayer, M.: Unified characterizations of minuscule Kac-Moody representations built from colored posets. arXiv: 1808.05200"}],"container-title":["Order"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-018-9473-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11083-018-9473-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-018-9473-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T21:54:18Z","timestamp":1775253258000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11083-018-9473-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,26]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,11]]}},"alternative-id":["9473"],"URL":"https:\/\/doi.org\/10.1007\/s11083-018-9473-4","relation":{},"ISSN":["0167-8094","1572-9273"],"issn-type":[{"value":"0167-8094","type":"print"},{"value":"1572-9273","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,26]]},"assertion":[{"value":"3 May 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 September 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 October 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}