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Introduction to Lattice Theory with Computer Science Applications by Vijay K. Garg

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Chapter 2Representing Posets

2.1 Introduction

We now look at some possible representations for efficient queries and operations on posets. For this purpose, we first examine some of the common operations that are generally performed on posets. Given a poset c02-math-0001, the following operations on elements c02-math-0002 are frequently performed:

  1. Check if c02-math-0003. We denote this operation by c02-math-0004.
  2. Check if c02-math-0005 covers c02-math-0006.
  3. Compute c02-math-0007 (c02-math-0008) and c02-math-0009 (c02-math-0010).

In all such representations, we first need to number the elements of the poset. A useful way ...

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