{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:59:37Z","timestamp":1778720377054,"version":"3.51.4"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2008,12,24]],"date-time":"2008-12-24T00:00:00Z","timestamp":1230076800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2009,12]]},"DOI":"10.1007\/s00454-008-9131-5","type":"journal-article","created":{"date-parts":[[2008,12,23]],"date-time":"2008-12-23T14:23:00Z","timestamp":1230042180000},"page":"705-721","source":"Crossref","is-referenced-by-count":6,"title":["Delannoy Orthants of Legendre Polytopes"],"prefix":"10.1007","volume":"42","author":[{"given":"G\u00e1bor","family":"Hetyei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2008,12,24]]},"reference":[{"issue":"2","key":"9131_CR1","doi-asserted-by":"crossref","first-page":"#R6","DOI":"10.37236\/1863","volume":"11","author":"C. Athanasiadis","year":"2004","unstructured":"Athanasiadis, C.: h *-Vectors, Eulerian polynomials and stable polytopes of graphs. Electron. J. Comb. 11(2), #R6 (2004), 13 pp","journal-title":"Electron. J. Comb."},{"issue":"1","key":"9131_CR2","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.jspi.2005.02.004","volume":"135","author":"C. Banderier","year":"2005","unstructured":"Banderier, C., Schwer, S.: Why Delannoy numbers? J.\u00a0Stat. Plan. Inference 135(1), 40\u201354 (2005)","journal-title":"J.\u00a0Stat. Plan. Inference"},{"key":"9131_CR3","volume-title":"An Introduction to Orthogonal Polynomials","author":"T.S. Chihara","year":"1978","unstructured":"Chihara, T.S.: An Introduction to Orthogonal Polynomials. Gordon and Breach, New York (1978)"},{"key":"9131_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-010-2196-8","volume-title":"Advanced Combinatorics","author":"L. Comtet","year":"1974","unstructured":"Comtet, L.: Advanced Combinatorics. Reidel, Dordrecht (1974)"},{"key":"9131_CR5","first-page":"70","volume":"24","author":"H. Delannoy","year":"1895","unstructured":"Delannoy, H.: Employ d\u2019\u00e9chiquier pour la r\u00e9solution de certains probl\u00e8mes de probabilit\u00e9s. Assoc. Franc. Bord. 24, 70\u201390 (1895)","journal-title":"Assoc. Franc. Bord."},{"key":"9131_CR6","unstructured":"Fong, W.: Triangulations and combinatorial properties of convex polytopes. PhD. Thesis, MIT (2000)"},{"key":"9131_CR7","first-page":"205","volume-title":"Arnold\u2013Gelfand Mathematical Seminars: Geometry and Singularity Theory","author":"I.M. Gelfand","year":"1996","unstructured":"Gelfand, I.M., Graev, M.I., Postnikov, A.: Combinatorics of hypergeometric functions associated with positive roots. In: Arnold\u2013Gelfand Mathematical Seminars: Geometry and Singularity Theory, pp.\u00a0205\u2013221. Birkh\u00e4user, Boston (1996)"},{"key":"9131_CR8","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1017\/S0305004100033168","volume":"54","author":"I.J. Good","year":"1958","unstructured":"Good, I.J.: Legendre polynomials and trinomial random walks. Proc. Camb. Philos. Soc. 54, 39\u201342 (1958)","journal-title":"Proc. Camb. Philos. Soc."},{"key":"9131_CR9","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.2140\/pjm.1957.7.1351","volume":"7","author":"I. Heller","year":"1957","unstructured":"Heller, I.: On linear systems with integral valued solutions. Pac. J. Math. 7, 1351\u20131364 (1957)","journal-title":"Pac. J. Math."},{"key":"9131_CR10","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.2140\/pjm.1962.12.1321","volume":"4","author":"I. Heller","year":"1962","unstructured":"Heller, I., Hoffman, A.J.: On unimodular matrices. Pac. J. Math. 4, 1321\u20131327 (1962)","journal-title":"Pac. J. Math."},{"key":"9131_CR11","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/s00026-006-0299-1","volume":"10","author":"G. Hetyei","year":"2006","unstructured":"Hetyei, G.: Central Delannoy numbers and balanced Cohen\u2013Macaulay complexes. Ann. Comb. 10, 443\u2013462 (2006)","journal-title":"Ann. Comb."},{"issue":"2","key":"9131_CR12","doi-asserted-by":"crossref","first-page":"#R4","DOI":"10.37236\/1861","volume":"11","author":"G. Hetyei","year":"2004","unstructured":"Hetyei, G.: Orthogonal polynomials represented by CW-spheres. Electron. J. Comb. 11(2), #R4 (2004), 28 pp","journal-title":"Electron. J. Comb."},{"key":"9131_CR13","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/j.jcta.2007.07.007","volume":"115","author":"G. Hetyei","year":"2008","unstructured":"Hetyei, G.: Tchebyshev triangulations of stable simplicial complexes. J.\u00a0Comb. Theory. Ser. A 115, 569\u2013592 (2008)","journal-title":"J.\u00a0Comb. Theory. Ser. A"},{"key":"9131_CR14","doi-asserted-by":"crossref","first-page":"193","DOI":"10.2307\/3608257","volume":"36","author":"D.F. Lawden","year":"1952","unstructured":"Lawden, D.F.: On the solution of a linear difference equation. Math. Gaz. 36, 193\u2013196 (1952)","journal-title":"Math. Gaz."},{"key":"9131_CR15","first-page":"223","volume":"26","author":"L. Moser","year":"1963","unstructured":"Moser, L., Zayachkowski, W.: Lattice paths with diagonal steps. Scr. Math. 26, 223\u2013229 (1963)","journal-title":"Scr. Math."},{"key":"9131_CR16","unstructured":"Postnikov, A.: Permutohedra, associahedra, and beyond. Preprint (2005). arXiv:math.CO\/0507163"},{"key":"9131_CR17","unstructured":"Sloane, N.J.A.: On-Line Encyclopedia of Integer Sequences. http:\/\/www.research.att.com\/~njas\/sequences"},{"key":"9131_CR18","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/S0167-5060(08)70717-9","volume":"6","author":"R.P. Stanley","year":"1980","unstructured":"Stanley, R.P.: Decompositions of rational convex polytopes. Ann. Discrete Math. 6, 333\u2013342 (1980)","journal-title":"Ann. Discrete Math."},{"key":"9131_CR19","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511609589","volume-title":"Enumerative Combinatorics","author":"R.P. Stanley","year":"1999","unstructured":"Stanley, R.P.: Enumerative Combinatorics, vol.\u00a0II. Cambridge University Press, Cambridge (1999)"},{"key":"9131_CR20","unstructured":"Sulanke, R.A.: Objects counted by the central Delannoy numbers. J. Integer Seq. 6, Article 03.1.5 (2003), 19 pp"},{"key":"9131_CR21","doi-asserted-by":"crossref","first-page":"433","DOI":"10.2748\/tmj\/1163775139","volume":"58","author":"S. Sullivant","year":"2006","unstructured":"Sullivant, S.: Compressed polytopes and statistical disclosure limitation. Tohoku Math. J. 58, 433\u2013445 (2006)","journal-title":"Tohoku Math. J."},{"key":"9131_CR22","volume-title":"Generating Functionology","author":"H.S. Wilf","year":"1994","unstructured":"Wilf, H.S.: Generating Functionology. Academic Press, San Diego (1994)"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-008-9131-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-008-9131-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-008-9131-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,14]],"date-time":"2020-05-14T02:18:44Z","timestamp":1589422724000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-008-9131-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12,24]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,12]]}},"alternative-id":["9131"],"URL":"https:\/\/doi.org\/10.1007\/s00454-008-9131-5","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,12,24]]}}}