{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,2,10]],"date-time":"2023-02-10T20:51:10Z","timestamp":1676062270652},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2008,5,1]],"date-time":"2008-05-01T00:00:00Z","timestamp":1209600000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2008,5]]},"abstract":"<jats:p>We derive here the Friedland\u2013Tverberg inequality for positive hyperbolic polynomials. This inequality is applied to give lower bounds for the number of matchings in r-regular bipartite graphs. It is shown that some of these bounds are asymptotically sharp. We improve the known lower bound for the three-dimensional monomer\u2013dimer entropy.<\/jats:p>","DOI":"10.1017\/s0963548307008747","type":"journal-article","created":{"date-parts":[[2007,9,28]],"date-time":"2007-09-28T10:05:07Z","timestamp":1190973907000},"page":"347-361","source":"Crossref","is-referenced-by-count":6,"title":["Lower Bounds for Partial Matchings in Regular Bipartite Graphs and Applications to the Monomer\u2013Dimer Entropy"],"prefix":"10.1017","volume":"17","author":[{"given":"SHMUEL","family":"FRIEDLAND","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LEONID","family":"GURVITS","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2008,5,1]]},"reference":[{"key":"S0963548307008747_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2004.08.005"},{"key":"S0963548307008747_ref8","unstructured":"[8] Friedland S. and Gurvits L. (2006) Generalized Friedland-Tverberg inequality: Applications and extensions. arXiv:math\/0603410 v2."},{"key":"S0963548307008747_ref14","doi-asserted-by":"publisher","DOI":"10.1145\/1132516.1132578"},{"key":"S0963548307008747_ref6","doi-asserted-by":"publisher","DOI":"10.2307\/1971250"},{"key":"S0963548307008747_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(02)00715-2"},{"key":"S0963548307008747_ref9","unstructured":"[9] Friedland S. , Krop E. , Lundow P. H. and Markstr\u00f6m K. (2007) Validations of the asymptotic matching conjectures. arXiv:math.CO\/0603001 v1."},{"key":"S0963548307008747_ref21","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-10669"},{"key":"S0963548307008747_ref4","first-page":"459","article-title":"On random matrices II","volume":"3","author":"Erd\u0151s","year":"1968","journal-title":"Studia Math. Hungar."},{"key":"S0963548307008747_ref22","first-page":"117","article-title":"Aufgabe 45","volume":"35","author":"van der Waerden","year":"1926","journal-title":"Jahresber. Deutsch. Math.-Verein."},{"key":"S0963548307008747_ref2","first-page":"945","article-title":"Some properties of nonnegative matrices and their permanents","volume":"14","author":"Bregman","year":"1973","journal-title":"Soviet Math. Dokl."},{"key":"S0963548307008747_ref15","first-page":"125","volume-title":"Research Papers in Statistics: Festschrift for J. Neyman","author":"Hammersley","year":"1966"},{"key":"S0963548307008747_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/1385-7258(80)90043-8"},{"key":"S0963548307008747_ref7","doi-asserted-by":"publisher","DOI":"10.1080\/03081088208817436"},{"key":"S0963548307008747_ref1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1664623"},{"key":"S0963548307008747_ref17","volume-title":"North-Holland Mathematical Studies","author":"Lov\u00e1sz","year":"1986"},{"key":"S0963548307008747_ref3","first-page":"854","article-title":"Proof of the van der Waerden conjecture for permanents","volume":"22","author":"Egorichev","year":"1981","journal-title":"Siberian Math. J."},{"key":"S0963548307008747_ref18","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1997.1798"},{"key":"S0963548307008747_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01877590"},{"key":"S0963548307008747_ref10","unstructured":"[10] Friedland S. , Krop E. and Markstr\u00f6m K. Enumerating matchings in regular graphs, in preparation."},{"key":"S0963548307008747_ref5","first-page":"475","article-title":"Proof of the van der Waerden conjecture regarding the permanent of doubly stochastic matrix","volume":"29","author":"Falikman","year":"1981","journal-title":"Math. Notes Acad. Sci. USSR"},{"key":"S0963548307008747_ref13","unstructured":"[13] Gurvits L. (2004) Combinatorial and algorithmic aspects of hyperbolic polynomials. arXIv: math.CO\/0404474."},{"key":"S0963548307008747_ref20","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177703591"},{"key":"S0963548307008747_ref12","unstructured":"[12] Friedland S. and Peled U. N. The pressure associated with multidimensional SOFT. In preparation."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548307008747","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,9]],"date-time":"2019-04-09T16:35:15Z","timestamp":1554827715000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548307008747\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,5]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,5]]}},"alternative-id":["S0963548307008747"],"URL":"https:\/\/doi.org\/10.1017\/s0963548307008747","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,5]]}}}