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Chapter 14Graph Enumeration B: Lec 18
14.3 Burnside’s Lemma14.4 Cycle-Index Polynomial of a Permutation Group
1 c 2010 by Jonathan L. Gross
2 Chapter 14 Graph Enumeration B: Lec 18
14.3 BURNSIDE’S LEMMA
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Section 14.3 Burnside’s Lemma 3
Stabilizer of an Object
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4 Chapter 14 Graph Enumeration B: Lec 18
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Section 14.3 Burnside’s Lemma 5
Fixed-Point Set of a Permutation
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6 Chapter 14 Graph Enumeration B: Lec 18
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Section 14.3 Burnside’s Lemma 7
Stabilizers and Fixed-Point Sets
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8 Chapter 14 Graph Enumeration B: Lec 18
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Section 14.3 Burnside’s Lemma 9
Relationship Between Stabilizers and Orbits
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10 Chapter 14 Graph Enumeration B: Lec 18
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Section 14.3 Burnside’s Lemma 11
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12 Chapter 14 Graph Enumeration B: Lec 18
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Section 14.3 Burnside’s Lemma 13
Fig 14.3.1
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14 Chapter 14 Graph Enumeration B: Lec 18
Proof of Burnside’s Lemma
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Section 14.3 Burnside’s Lemma 15
Direct Application of Burnside’s Lemma
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16 Chapter 14 Graph Enumeration B: Lec 18
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Section 14.4 Cycle-Index of a Perm Group 17
14.4 CYCLE-INDEX OF A PERM GROUP
Cycle-Structure Monomial of a Permutation
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18 Chapter 14 Graph Enumeration B: Lec 18
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Section 14.4 Cycle-Index of a Perm Group 19
Cycle-Index Polynomial
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20 Chapter 14 Graph Enumeration B: Lec 18
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Section 14.4 Cycle-Index of a Perm Group 21
Correctness of Substituting Into the Cycle-Index Polynomial
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22 Chapter 14 Graph Enumeration B: Lec 18
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Section 14.4 Cycle-Index of a Perm Group 23
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24 Chapter 14 Graph Enumeration B: Lec 18
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Section 14.4 Cycle-Index of a Perm Group 25
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26 Chapter 14 Graph Enumeration B: Lec 18
14.7 SUPPLEMENTARY EXERCISES
c 2010 by Jonathan L. Gross