✦ LIBER ✦
Factoring, into Edge Transpositions of a Tree, Permutations Fixing a Terminal Vertex
✍ Scribed by John H. Smith
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 71 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
✦ Synopsis
If the symmetric group is generated by transpositions corresponding to the edges of a spanning tree we discuss identities they satisfy, including a set of defining relations. We further show that a minimal length factorization of a permutation fixing a terminal vertex does not involve the unique edge incident to that vertex.
1999 Academic Press
Proof. 1 and 2 are clear, as are cases k=1, k=2 of 4 from which the case k=2 of 3 follows. To prove 3 in for general k insert two a 1 just before