{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T13:54:27Z","timestamp":1716904467490},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,9,4]],"date-time":"2021-09-04T00:00:00Z","timestamp":1630713600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,9,4]],"date-time":"2021-09-04T00:00:00Z","timestamp":1630713600000},"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":["Math.Comput.Sci."],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s11786-021-00518-z","type":"journal-article","created":{"date-parts":[[2021,9,4]],"date-time":"2021-09-04T03:25:55Z","timestamp":1630725955000},"page":"889-898","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Column-Convex and Convex Carlitz Polyominoes"],"prefix":"10.1007","volume":"15","author":[{"given":"Toufik","family":"Mansour","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reza","family":"Rastegar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Armend Sh.","family":"Shabani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,9,4]]},"reference":[{"key":"518_CR1","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1080\/00029890.1954.11988548","volume":"61","author":"SW Golomb","year":"1954","unstructured":"Golomb, S.W.: Checker boards and polyominoes. Am. Math. Monthly 61, 675\u2013682 (1954)","journal-title":"Am. Math. Monthly"},{"issue":"7","key":"518_CR2","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1088\/0305-4470\/16\/7\/003","volume":"16","author":"V Hakim","year":"1983","unstructured":"Hakim, V., Nadal, J.P.: Exact results for 2D directed animals on a strip of finite width. J. Phys. A Math. Gen. 16(7), 213\u2013218 (1983)","journal-title":"J. Phys. A Math. Gen."},{"key":"518_CR3","doi-asserted-by":"publisher","first-page":"1091","DOI":"10.1007\/BF01014901","volume":"51:5\u20136","author":"V Privman","year":"1988","unstructured":"Privman, V., Svrakic, N.M.: Difference equations in statistical mechanics. I. Cluster statistics models. J. Stat. Phys. 51:5\u20136, 1091\u20131110 (1988)","journal-title":"J. Stat. Phys."},{"key":"518_CR4","volume-title":"Directed models of polymers, interfaces, and clusters: scaling and finite-size properties","author":"V Privman","year":"1989","unstructured":"Privman, V., Svrakic, N.M.: Directed models of polymers, interfaces, and clusters: scaling and finite-size properties. Springer, Berlin (1989)"},{"issue":"21\u2013122","key":"518_CR5","first-page":"225","volume":"1","author":"G Viennot","year":"1985","unstructured":"Viennot, G.: Probl\u00e9mes combinatoires pos\u00e9s par la physique statistique. Ast\u00e9risque 1(21\u2013122), 225\u2013246 (1985)","journal-title":"Ast\u00e9risque"},{"key":"518_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRev.103.1","volume":"103","author":"HNV Temperley","year":"1956","unstructured":"Temperley, H.N.V.: Combinatorial problems suggested by the statistical mechanics of domains and of rubber-like molecules. Phys. Rev. 103, 1\u201316 (1956)","journal-title":"Phys. Rev."},{"issue":"1","key":"518_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0925-7721(94)00015-N","volume":"5","author":"D Beauquier","year":"1995","unstructured":"Beauquier, D., Nivat, M., Remila, \u00c9., Robson, M.: Tiling figures of the plane with two bars. Comput. Geometry. Theory Appl. 5(1), 1\u201325 (1995)","journal-title":"Comput. Geometry. Theory Appl."},{"key":"518_CR8","first-page":"72","volume":"66","author":"R Berger","year":"1966","unstructured":"Berger, R.: The undecidability of the domino problem. Memoirs Am. Math. Soc. 66, 72 (1966)","journal-title":"Memoirs Am. Math. Soc."},{"key":"518_CR9","volume-title":"Tilings and patterns","author":"B Gr\u00fcnbaum","year":"1989","unstructured":"Gr\u00fcnbaum, B., Shephard, G.C.: Tilings and patterns. W.H. Freeman and Company, New York (1989)"},{"issue":"2","key":"518_CR10","first-page":"156","volume":"29","author":"DA Klarner","year":"1981","unstructured":"Klarner, D.A.: My life among the polyominoes. Nieuw Archief voor Wiskunde. Derde Serie 29(2), 156\u2013177 (1981)","journal-title":"Nieuw Archief voor Wiskunde. Derde Serie"},{"key":"518_CR11","first-page":"9","volume":"3","author":"DA Klarner","year":"1965","unstructured":"Klarner, D.A.: Some results concerning polyominoes. Fib. Quart. 3, 9\u201320 (1965)","journal-title":"Fib. Quart."},{"key":"518_CR12","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/S0021-9800(69)80044-X","volume":"7","author":"DA Klarner","year":"1969","unstructured":"Klarner, D.A.: Packing a rectangle with congruent $$n$$-ominoes. J. Combin. Theory 7, 107\u2013115 (1969)","journal-title":"J. Combin. Theory"},{"key":"518_CR13","unstructured":"Barcucci, E., Frosini, A., Rinaldi, S.: Direct-convex polyominoes: ECO method and bijective results. Proc. Formal Power Ser. Algeb. Combin. Melbourne (2002)"},{"issue":"2","key":"518_CR14","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1088\/0305-4470\/28\/2\/011","volume":"28","author":"A Conway","year":"1995","unstructured":"Conway, A.: Enumerating $$2D$$ percolation series by the finite-lattice method: theory. J. Phys. A 28(2), 335\u2013349 (1995)","journal-title":"J. Phys. A"},{"key":"518_CR15","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/0304-3975(84)90116-6","volume":"34","author":"M Delest","year":"1984","unstructured":"Delest, M., Viennot, X.G.: Algebraic languages and polyominoes enumeration. Theoret. Comput. Sci. 34, 169\u2013206 (1984)","journal-title":"Theoret. Comput. Sci."},{"key":"518_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-9927-4","volume-title":"Polygons, Polyominoes and Polycubes","author":"AJ Guttmann","year":"2009","unstructured":"Guttmann, A.J.: Polygons, Polyominoes and Polycubes. Springer, Netherlands (2009)"},{"key":"518_CR17","unstructured":"Viennot, X.G.: A survey of polyominoes enumeration. In: Proceedings of the 4th FPSAC Publications du LACIM, Institut Mittag-Leffler 11, 399\u2013420 (1992)"},{"key":"518_CR18","doi-asserted-by":"crossref","unstructured":"A. Del Lungo, M. Mirolli, R. Pinzani, S. Rinaldi: A bijection for directed-convex polyominoes. In: Proceedings of the DM-CCG 2001, Discrete Mathematics and Theoretical Computer Science AA, pp. 133\u2013144 (2001)","DOI":"10.46298\/dmtcs.2298"},{"issue":"3\u20134","key":"518_CR19","doi-asserted-by":"publisher","first-page":"865","DOI":"10.1023\/A:1004855020556","volume":"102","author":"I Jensen","year":"2001","unstructured":"Jensen, I.: Enumerations of lattice animals and trees. J. Stat. Phys. 102(3\u20134), 865\u2013881 (2001)","journal-title":"J. Stat. Phys."},{"issue":"29","key":"518_CR20","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1088\/0305-4470\/33\/29\/102","volume":"33","author":"I Jensen","year":"2000","unstructured":"Jensen, I., Guttmann, A.J.: Statistics of lattice animals (polyominoes) and polygons. J. Phys. A 33(29), 257\u2013263 (2000)","journal-title":"J. Phys. A"},{"issue":"7","key":"518_CR21","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1080\/10236198.2020.1813730","volume":"26","author":"T Mansour","year":"2021","unstructured":"Mansour, T., Rastegar, R.: Convex polyominoes revisited: enumeration of outer site perimeter, interior vertices, and boundary vertices of certain degrees. J. Diff. Eq. Appl. 26(7), 1013\u20131041 (2021)","journal-title":"J. Diff. Eq. Appl."},{"key":"518_CR22","unstructured":"S. Fereti\u0107, D. Svrtan: On the number of column-convex polyominoes with given perimeter and number of columns. In: Proceedings of the 5th FPSAC, Firenze pp. 201\u2013214 (1993)"},{"key":"518_CR23","first-page":"57","volume":"9","author":"S Fereti\u0107","year":"2007","unstructured":"Fereti\u0107, S.: A perimeter enumeration of column-convex polyominoes. Disc. Math. Theoret. Comput. Sci. 9, 57\u201384 (2007)","journal-title":"Disc. Math. Theoret. Comput. Sci."},{"key":"518_CR24","doi-asserted-by":"publisher","first-page":"#111731","DOI":"10.1016\/j.disc.2019.111731","volume":"343:3","author":"A Boussicault","year":"2020","unstructured":"Boussicault, A., Rinaldi, S., Socci, S.: The number of directed $$k$$-convex polyominoes. Disc. Math. 343:3, #111731 (2020)","journal-title":"Disc. Math."},{"key":"518_CR25","unstructured":"T. Mansour, A. Sh. Shabani: Smooth Column Convex Polyominoes, Submitted"},{"issue":"1\u20133","key":"518_CR26","first-page":"29","volume":"246","author":"C Banderier","year":"2000","unstructured":"Banderier, C., Bousquet-M\u00e9lou, M., Denise, A., Flajolet, P., Gardy, D., Gouyou-Beauchamps, D.: Generating functions for generating trees. Disc. Math. 246(1\u20133), 29\u201355 (2000)","journal-title":"Disc. Math."},{"key":"518_CR27","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801655","volume-title":"Analytic Combinatorics","author":"P Flajolet","year":"2009","unstructured":"Flajolet, P., Sedgewick, R.: Analytic Combinatorics. Cambridge University Press, Cambridge (2009)"},{"key":"518_CR28","unstructured":"N. Caki\u0107, T. Mansour, G. Y\u0131ld\u0131r\u0131m: A decomposition of column-convex polyominoes and two vertex statistics, preprint"}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-021-00518-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11786-021-00518-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-021-00518-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,9]],"date-time":"2021-10-09T04:24:08Z","timestamp":1633753448000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11786-021-00518-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,4]]},"references-count":28,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["518"],"URL":"https:\/\/doi.org\/10.1007\/s11786-021-00518-z","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"value":"1661-8270","type":"print"},{"value":"1661-8289","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,4]]},"assertion":[{"value":"31 January 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 July 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 September 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}