{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T11:19:52Z","timestamp":1761218392232,"version":"3.37.3"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T00:00:00Z","timestamp":1624233600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T00:00:00Z","timestamp":1624233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,9]]},"DOI":"10.1007\/s00454-021-00314-3","type":"journal-article","created":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T14:02:50Z","timestamp":1624284170000},"page":"464-474","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Binomial Inequalities for Chromatic, Flow, and Tension Polynomials"],"prefix":"10.1007","volume":"66","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8889-785X","authenticated-orcid":false,"given":"Matthias","family":"Beck","sequence":"first","affiliation":[]},{"given":"Emerson","family":"Le\u00f3n","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,6,21]]},"reference":[{"key":"314_CR1","doi-asserted-by":"crossref","unstructured":"Athanasiadis, C.A.: $$h^\\ast $$-Vectors, Eulerian polynomials and stable polytopes of graphs. Electron. J. Comb. 11(2), #\u00a0R6 (2004\/06)","DOI":"10.37236\/1863"},{"key":"314_CR2","volume-title":"Computing the Continuous Discretely. Integer-Point Enumeration in Polyhedra. Undergraduate Texts in Mathematics","author":"M Beck","year":"2015","unstructured":"Beck, M., Robins, S.: Computing the Continuous Discretely. Integer-Point Enumeration in Polyhedra. Undergraduate Texts in Mathematics. Springer, New York (2015)"},{"issue":"4","key":"314_CR3","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/BF01312545","volume":"99","author":"U Betke","year":"1985","unstructured":"Betke, U., McMullen, P.: Lattice points in lattice polytopes. Monatsh. Math. 99(4), 253\u2013265 (1985)","journal-title":"Monatsh. Math."},{"issue":"2","key":"314_CR4","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1090\/S0002-9947-1992-1069745-7","volume":"332","author":"F Brenti","year":"1992","unstructured":"Brenti, F.: Expansions of chromatic polynomials and log-concavity. Trans. Am. Math. Soc. 332(2), 729\u2013756 (1992)","journal-title":"Trans. Am. Math. Soc."},{"issue":"3","key":"314_CR5","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/s10801-010-0254-4","volume":"33","author":"F Breuer","year":"2011","unstructured":"Breuer, F., Dall, A.: Bounds on the coefficients of tension and flow polynomials. J. Algebraic Comb. 33(3), 465\u2013482 (2011)","journal-title":"J. Algebraic Comb."},{"issue":"1\u20132","key":"314_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00209-010-0782-6","volume":"270","author":"F Breuer","year":"2012","unstructured":"Breuer, F., Sanyal, R.: Ehrhart theory, modular flow reciprocity, and the Tutte polynomial. Math. Z. 270(1\u20132), 1\u201318 (2012)","journal-title":"Math. Z."},{"key":"314_CR7","volume-title":"Triangulations. Algorithms and Computation in Mathematics","author":"JA De Loera","year":"2010","unstructured":"De Loera, J.A., Rambau, J., Santos, F.: Triangulations. Algorithms and Computation in Mathematics, vol. 25. Springer, Berlin (2010)"},{"key":"314_CR8","first-page":"616","volume":"254","author":"E Ehrhart","year":"1962","unstructured":"Ehrhart, E.: Sur les poly\u00e8dres rationnels homoth\u00e9tiques \u00e0 $$n$$ dimensions. C. R. Acad. Sci. Paris 254, 616\u2013618 (1962)","journal-title":"C. R. Acad. Sci. Paris"},{"issue":"1","key":"314_CR9","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1080\/03081088708817823","volume":"22","author":"ER Gansner","year":"1987","unstructured":"Gansner, E.R., Vo, K.P.: The chromatic generating function. Linear Multilinear Algebra 22(1), 87\u201393 (1987)","journal-title":"Linear Multilinear Algebra"},{"issue":"1\u20133","key":"314_CR10","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/S0012-365X(00)00344-7","volume":"232","author":"IM Gessel","year":"2001","unstructured":"Gessel, I.M.: Acyclic orientations and chromatic generating functions. Discret. Math. 232(1\u20133), 119\u2013130 (2001)","journal-title":"Discret. Math."},{"key":"314_CR11","unstructured":"Haase, C., Paffenholz, A., Piechnik, L.C., Santos, F.: Existence of unimodular triangulations\u2014positive results (2014). arXiv:1405.1687"},{"issue":"2","key":"314_CR12","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/s10801-007-0086-z","volume":"27","author":"P Hersh","year":"2008","unstructured":"Hersh, P., Swartz, E.: Coloring complexes and arrangements. J. Algebraic Comb. 27(2), 205\u2013214 (2008)","journal-title":"J. Algebraic Comb."},{"key":"314_CR13","unstructured":"Jaeger, F.: Nowhere-zero flow problems. In: Selected Topics in Graph Theory, vol.\u00a03, pp. 71\u201395. Academic Press, San Diego (1988)"},{"issue":"2","key":"314_CR14","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1006\/jctb.2001.2081","volume":"84","author":"M Kochol","year":"2002","unstructured":"Kochol, M.: Polynomials associated with nowhere-zero flows. J. Comb. Theory Ser. B 84(2), 260\u2013269 (2002)","journal-title":"J. Comb. Theory Ser. B"},{"issue":"3","key":"314_CR15","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1002\/jgt.10038","volume":"40","author":"M Kochol","year":"2002","unstructured":"Kochol, M.: Tension polynomials of graphs. J. Graph Theory 40(3), 137\u2013146 (2002)","journal-title":"J. Graph Theory"},{"issue":"2","key":"314_CR16","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1016\/0095-8956(78)90015-1","volume":"24","author":"RR Korfhage","year":"1978","unstructured":"Korfhage, R.R.: $$\\sigma $$-Polynomials and graph coloring. J. Comb. Theory Ser. B 24(2), 137\u2013153 (1978)","journal-title":"J. Comb. Theory Ser. B"},{"issue":"3","key":"314_CR17","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/s00454-006-1294-3","volume":"38","author":"T Lam","year":"2007","unstructured":"Lam, T., Postnikov, A.: Alcoved polytopes, I. Discret. Comput. Geom. 38(3), 453\u2013478 (2007)","journal-title":"Discret. Comput. Geom."},{"key":"314_CR18","unstructured":"Le\u00f3n, E.: Stapledon decompositions and inequalities for coefficients of chromatic polynomials. S\u00e9m. Lothar. Combin. 78B, #\u00a024 (2017)"},{"issue":"1","key":"314_CR19","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/0012-365X(86)90191-3","volume":"58","author":"N Linial","year":"1986","unstructured":"Linial, N.: Graph coloring and monotone functions on posets. Discret. Math. 58(1), 97\u201398 (1986)","journal-title":"Discret. Math."},{"key":"314_CR20","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1112\/jlms\/s2-4.1.181","volume":"4","author":"IG Macdonald","year":"1971","unstructured":"Macdonald, I.G.: Polynomials associated with finite cell-complexes. J. Lond. Math. Soc. 4, 181\u2013192 (1971)","journal-title":"J. Lond. Math. Soc."},{"issue":"3","key":"314_CR21","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/s00454-007-9002-5","volume":"40","author":"S Payne","year":"2008","unstructured":"Payne, S.: Ehrhart series and lattice triangulations. Discret. Comput. Geom. 40(3), 365\u2013376 (2008)","journal-title":"Discret. Comput. Geom."},{"key":"314_CR22","unstructured":"Seymour, P.D.: Nowhere-zero flows. In: Handbook of Combinatorics, vol.\u00a01, pp. 289\u2013299. Elsevier, Amsterdam (1995)"},{"key":"314_CR23","unstructured":"Stanley, R.P.: A chromatic-like polynomial for ordered sets. In: 2nd Chapel Hill Conference on Combinatorial Mathematics and its Applications (Chapel Hill 1970), pp. 421\u2013427. Univ. North Carolina, Chapel Hill (1970)"},{"key":"314_CR24","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/S0167-5060(08)70717-9","volume":"6","author":"RP Stanley","year":"1980","unstructured":"Stanley, R.P.: Decompositions of rational convex polytopes. Ann. Discret. Math. 6, 333\u2013342 (1980)","journal-title":"Ann. Discret. Math."},{"issue":"1","key":"314_CR25","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. Discret. Comput. Geom. 1(1), 9\u201323 (1986)","journal-title":"Discret. Comput. Geom."},{"key":"314_CR26","unstructured":"Stanley, R.P.: Enumerative Combinatorics, vol.\u00a01. Cambridge Studies in Advanced Mathematics, vol. 49. Cambridge University Press, Cambridge (2012)"},{"issue":"10","key":"314_CR27","doi-asserted-by":"publisher","first-page":"5615","DOI":"10.1090\/S0002-9947-09-04776-X","volume":"361","author":"A Stapledon","year":"2009","unstructured":"Stapledon, A.: Inequalities and Ehrhart $$\\delta $$-vectors. Trans. Am. Math. Soc. 361(10), 5615\u20135626 (2009)","journal-title":"Trans. Am. Math. Soc."},{"issue":"3","key":"314_CR28","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/0012-365X(87)90109-9","volume":"66","author":"I Tomescu","year":"1987","unstructured":"Tomescu, I.: Graphical Eulerian numbers and chromatic generating functions. Discret. Math. 66(3), 315\u2013318 (1987)","journal-title":"Discret. Math."},{"key":"314_CR29","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1017\/S0305004100023173","volume":"43","author":"WT Tutte","year":"1947","unstructured":"Tutte, W.T.: A ring in graph theory. Proc. Camb. Philos. Soc. 43, 26\u201340 (1947)","journal-title":"Proc. Camb. Philos. Soc."},{"key":"314_CR30","unstructured":"Wilf, H.S.: Which polynomials are chromatic? In: Colloquio Internazionale sulle Teorie Combinatorie (Roma 1973), vol.\u00a01. Atti dei Convegni Lincei, vol. 17, pp. 247\u2013256. Accad. Naz. Lincei, Rome (1976)"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-021-00314-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-021-00314-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-021-00314-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,29]],"date-time":"2021-07-29T14:08:43Z","timestamp":1627567723000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-021-00314-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,21]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["314"],"URL":"https:\/\/doi.org\/10.1007\/s00454-021-00314-3","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"type":"print","value":"0179-5376"},{"type":"electronic","value":"1432-0444"}],"subject":[],"published":{"date-parts":[[2021,6,21]]},"assertion":[{"value":"22 November 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 September 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 June 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}