CSci 271 Lecture Notes

Week Seven, Wednesday: Basics of Counting and Pigeonhole Principle

Basic Counting Principles

The sum rule.

The product rule.

The Inclusion-Exclusion Principle

Overlapping sets: cardinality of the union.

Tree Diagrams

Playoff outcomes.

Pigeonhole Principle

If the number of items to assign is greater than the number of slots to assign them to, then some slot will be assigned more than one item.

Generalized Pigeonhole Principle

Generalize the pigeonhole principle for multiples of slot set cardinality.

Some Elegant Applications of the Pigeonhole Principle

Theorem 3: increasing/decreasing subsequence length.

Homework Assignment

Assigned Wednesday, October 21, due Wednesday, October 28, at beginning of class.

Chapter 3.1: 2, 10.
Chapter 3.2: 5, 6.
Chapter 3.3: 2, 24.
Chapter 4.1: 2, 6.
Chapter 4.2: 6, 14.


This page established October 21, 1998; last updated October 23, 1998.