Farley, Jonathan David and Klippenstine, Ryan (2009) Distributive lattices of small width, II: A problem from Stanley's 1986 text Enumerative Combinatorics. Journal of Combinatorial Theory. Series A, 116 (6). pp. 1097-1119. ISSN 0097-3165 http://resolver.caltech.edu/CaltechAUTHORS:20090911-112341226
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Abstract
In Richard P. Stanley's 1986 text, Enumerative Combinatorics, the following problem is posed: Fix a natural number k. Consider the posets P of cardinality n such that, for 0<i<n, P has exactly k order ideals (down-sets) of cardinality i. Let fk(n) be the number of such posets. What is the generating function ∑f_3(n)x^n? In this paper, the problem is solved.
| Item Type: | Article |
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| Additional Information: | © 2008 Elsevier Inc. Received 11 December 2006. Available online 16 April 2009. We would like to thank Professor Michael Roddy of Brandon University; we would also like to thank the referee for her or his comments. |
| Subject Keywords: | Distributive lattice; Order ideal; (Partially) ordered set |
| Record Number: | CaltechAUTHORS:20090911-112341226 |
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20090911-112341226 |
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| Official Citation: | Jonathan David Farley, Ryan Klippenstine, Distributive lattices of small width, II: A problem from Stanley's 1986 text Enumerative Combinatorics, Journal of Combinatorial Theory, Series A, Volume 116, Issue 6, August 2009, Pages 1097-1119, ISSN 0097-3165, DOI: 10.1016/j.jcta.2008.08.007. (http://www.sciencedirect.com/science/article/B6WHS-4W3296H-1/2/7a9919d7134028c5aedf347d9d5bfb76) |
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 15775 |
| Collection: | CaltechAUTHORS |
| Deposited By: | Tony Diaz |
| Deposited On: | 02 Oct 2009 18:58 |
| Last Modified: | 26 Dec 2012 11:21 |
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