{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T10:57:03Z","timestamp":1762340223672,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2008,9,24]],"date-time":"2008-09-24T00:00:00Z","timestamp":1222214400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We have produced extended series for prudent self-avoiding walks on the square lattice. These are subsets of self-avoiding walks. We conjecture the exact growth constant and critical exponent for the walks, and show that the (anisotropic) generating function is almost certainly not differentiably-finite.<\/jats:p>","DOI":"10.3390\/e10030309","type":"journal-article","created":{"date-parts":[[2008,9,29]],"date-time":"2008-09-29T05:43:40Z","timestamp":1222667020000},"page":"309-318","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Prudent Self-Avoiding Walks"],"prefix":"10.3390","volume":"10","author":[{"given":"John C.","family":"Dethridge","sequence":"first","affiliation":[{"name":"ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia"}]},{"given":"Anthony J.","family":"Guttmann","sequence":"additional","affiliation":[{"name":"ARC Centre of Excellence for Mathematics and Statistics of Complex Systems, Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2008,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0012-365X(95)00003-F","article-title":"A method for the enumeration of various classes of column-convex polygons","volume":"154","year":"1996","journal-title":"Disc. Math."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bousquet-Me\u00e9lou, M. (2008). Families of prudent self-avoiding walks, [arXiv: math.CO 0804.4843v1].","DOI":"10.46298\/dmtcs.3627"},{"key":"ref_3","unstructured":"Duchi, E. (,  2005). On some classes of prudent walks. Proceedings of the FPSAC\u201905, Taormina, Italy."},{"key":"ref_4","unstructured":"Duchi, E. Personal communication."},{"key":"ref_5","unstructured":"Pre\u00e9a, P. (1997). Exterior self-avoiding walks on the square lattice, (manuscript)."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1088\/0305-4470\/20\/3\/030","article-title":"Self-directed walk: a Monte Carlo study in two dimensions","volume":"20","author":"Turban","year":"1987","journal-title":"J. Phys. A"},{"key":"ref_7","unstructured":"Rechnitzer, A. Personal communication."},{"key":"ref_8","unstructured":"Lebowitz, J., and Domb, C. (1989). Phase Transitions and Critical Phenomena, Academic Press. 234 p."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1103\/PhysRevLett.76.344","article-title":"On the solvability of some statistical mechanical systems","volume":"76","author":"Guttmann","year":"1996","journal-title":"Phys. Rev. Letters."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/S0196-8858(02)00534-1","article-title":"Haruspicy and anisotropic generating functions","volume":"30","author":"Rechnitzer","year":"2003","journal-title":"Advances in Applied Mathematics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0195-6698(80)80051-5","article-title":"Differentiably finite power series","volume":"1","author":"Stanley","year":"1980","journal-title":"European J. Combin"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Stanley, R. P. (1999). Enumerative Combinatorics, Cambridge University Press.","DOI":"10.1017\/CBO9780511609589"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/10\/3\/309\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:20:59Z","timestamp":1760221259000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/10\/3\/309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,24]]},"references-count":12,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2008,9]]}},"alternative-id":["e10030309"],"URL":"https:\/\/doi.org\/10.3390\/e10030309","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2008,9,24]]}}}