On a Conjecture of Stanley Depth of Squarefree Veronese Ideals

摘要

In this article, we partially confirm a conjecture, proposed by Cimpoeaş, Keller, Shen, Streib, and Young, on the Stanley depth of squarefree Veronese ideals I _{n, d} . This conjecture suggests that, for positive integers 1 ≤ d ≤ n, . Herzog, Vlădoiu, and Zheng established a connection between the Stanley depths of quotients of monomial ideals and interval partitions of certain associated posets. Based on this connection, Keller, Shen, Streib, and Young recently developed a useful combinatorial tool to analyze the interval partitions of the posets associated with the squarefree Veronese ideals. We modify their ideas and prove the above conjecture for . We also obtain a lower bound of sdepth(I _{n, d} ) for any 1 ≤ d ≤ n. Our results greatly improve Theorem 1.1 in [1313. Keller , M., Shen , Y., Streib , N., Young , S. (2011). On the Stanley depth of squarefree Veronese ideals. J. Algebraic Combin. 33(2):313-324.[CrossRef], [Web of Science ®]View all references], and moreover, our construction leads to a direct proof of this theorem without using graph theory.View full textDownload full textKey WordsInterval partition, Squarefree monomial ideal, Squarefree veronese ideal, Stanley depth2000 Mathematics Subject Classification06A07, 06A11, 05E99, 13C13, 13C15Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927872.2011.585190