✦ LIBER ✦

Posets in which every interval is a product of chains, and natural local actions of the symmetric group

✍ Scribed by David J. Grabiner

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 545 KB
Volume: 199
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00287-8

No coin nor oath required. For personal study only.

✦ Synopsis

Consider a graded poset P with maximal and minimal elements. If every interval of rank three in P is a product of chains, and for every interval [.L ~1 of rank at least four, the open interval (x, y) is connected, we show that the entire poset is a product of chains. This proves a conjecture of Stanley concerning the natural local action of the symmetric group on maximal chains in a graded poset. On a product of chains, the natural action is the permutation action on the multiset corresponding to the chains. The result implies that if every open interval is connected (which holds if the poset is Cohen-Macaulay, for example), the only possible such natural action is this multiset action.

📜 SIMILAR VOLUMES

The Production of oil of American Wormse

The Production of oil of American Wormseed, U. S. P., in Illinois**This investigation was undertaken because the supply of wormseed oil has been for several years vcry inadequate to the demand, and this condition has prevented extensive use of the oil in the treatment of domestic animals—a field in which it is much needed. Owing to the low individual value of such animals as hogs, for example, it is not economical to treat them with a drug of such high price as wormseed oil. This paper is a report of the first year’s work in producing this oil at the Experiment Station of the Moorman Mfg. Co., Quincy, Ill. It is planned to continue the work on a much larger scale, covering every phase of the problem. Anyone wishing to produce the oil can obtain the full cooperation of this company on request.

✍ Konantz, W.A. 📂 Article 📅 1924 🏛 Elsevier ⚖ 408 KB 👁 2 views