MATH 310, FALL 2003 Combinatorial Problem Solving Lecture 34, Friday, November 21

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MATH 310, FALL 2003(Combinatorial Problem
Solving)Lecture 34, Friday, November 21
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7.1. Recurrence Relation Models

• Homework (MATH 31010W)
• Read 7.1
• Do 6.5 all odd numbered problems
• Turn in 6.5 2,4,6,8
• Turn in 7.1 2,4,6,12,16,18,26,48

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Test 1 2 - Statistics

• Here is a stem-and-leaf report on the total.
• Median 187
• (Bonus points are not counted.)

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Test 2 - Statistics

• Here is a stem-and-leaf report on the test.
• Median 94
• There are is only one mark.

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Test 2 Problem 1

• Median 0

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Test 2 Problem 2

• Median -1

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Test 2 Problem 3

• Median -3

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Test 2 Problem 4

• Median -2

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Test 2 Problem 4

• Median -2

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Test 2 Problem 4

• Median -2

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Test 2 Problem 5

• Median -5

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Test 2 Problem 6

• Median -3

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Test 2 Problem 7

• Median 0

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Test 2 Problem 8

• Median -2

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Test 2 Problem 9

• Median -4

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Test 2 Problem 10

• Median -1

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Test 2 Problem 11

• Median -7

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Recurrence Relation

• an c1an-1 c2an-2 ... cran-r.
• an can-1 f(n).
• an a0an-1 a1an-2 ... an-2a1 an-1a0.
• an,m an-1,m an,m-1.
• Initial Conditions.
• an an-1 an-2, a0 2, a1 3.

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Example 1 Arrangements

• Find a recurrence relation for the number of ways
  to arrange n objects in a row.
• an nan-1.
• a0 1.

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Example 2 Climbing Stairs

• n stairs to climb
• each step can cover either 1 step or 2 steps.
• Find a recurrence relation for an, the number of
  ways to climb the stairs.
• an an-1an-2.
• a0 a1 1.