P(n,k)的一个单调性定理

给出无序分拆数P(n,k)的一个单调性定理。

Analyzing the safety of removal sequences for piles of an offshore jacket platform

An inevitable consequence of the development of the offshore petroleum industry is the eventual obsolescence of large offshore structures. Proper methods for removal of decommissioned offshore platforms are becoming an important topic that the oil and gas industry must pay increasing attention to. While removing sections from a decommissioned jacket platform, the stability of the remaining parts is critical The jacket danger indices D ~ and Ds defined in this paper are very useful for analyzing the safety of any procedure planned for disassembling a jacket platform. The safest piles cutting sequence can be determined easily by comparing every column of Do and Ds or simply analyzing the figures of every row ofD o and D,.

P(n,k)的计数及其良域

设Ｐ（ｎ，ｋ）为整数ｎ分ｋ部的无序分拆的个数，每个分部≥１；Ｐ（ｎ）为ｎ的全分拆的个数．Ｐ（ｎ，ｋ）是用途广泛的、且又十分难予计算的数．本文证明了下述定理：当ｎ＜ｋ，Ｐ（ｎ，ｋ）＝０；当ｋ≤ｎ≤２ｋ，Ｐ（ｎ－ｋ）；当 ｋ＝１，４≤ｎ≤５，或者当ｋ≥２，２ｋ＋１≤ｎ≤３ｋ＋２，Ｐ（ｎ，ｋ）－Ｐ（ｔ）。还定义了Ｐ（ｎ，ｋ）的良域，因而可借助若干个Ｐ（ｎ）的值，迅速地计算大量的Ｐ（ｎ，ｋ）的值。