B 38 Recall The Partially Ordered Set Ii Of All Partitions Of 1 2 N Where The Partial Order Is That Of Refine 1 (569.21 KiB) Viewed 37 times
B 38. Recall the partially ordered set II, of all partitions of {1, 2, ...,n}, where the partial order is that of refinement (see Exercise 47 of Chapter 4). Determine the Möbius functions of I13 and II4.
47. Let II, denote the set of all partitions of the set {1,2,...,n} into nonempty sets. Given two partitions 7 and o in IIn, define a <o, provided that each part of a is contained in a part of o. Thus, the partition a can be obtained by partitioning the parts of o. This relation is usually expressed by saying that n is a refinement of o.
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!