Skip to Main Content
Combinatorics of Permutations, 2nd Edition
book

Combinatorics of Permutations, 2nd Edition

by Miklos Bona
April 2016
Intermediate to advanced content levelIntermediate to advanced
478 pages
14h 44m
English
Chapman and Hall/CRC
Content preview from Combinatorics of Permutations, 2nd Edition
366 Combinatorics of Permutations, Second Edition
s in the traditional sense.
PROPOSITION 9.17
Let a, b,andz
be defined as above, and let s
=(12···(n +1))z
.Thenwe
have
1. c(Γ(s
)) = c(Γ(s)) 1 if 2 a,anda 1 and z(1) are not in the same
cycle of s,
2. c(Γ(s
)) = c(Γ(s)) + 1 if 2 a,anda 1 and z(1) are in the same cycle
of s,and
3. c(Γ(s
)) = c(Γ(s)) + 1 if a =1.
PROOF Let us assume first that a 2, and that a 1 is in a cycle C
1
of s,andz(1) is in a different cycle C
2
of s.LetC
1
=((a 1)b ···) and let
C
2
=(z(1) ···n). After the insertion of n+1 into z, the obtained permutation
s
=(12···(n +1))z
sends a 1ton +1, then n +1 to z(1), then leaves the
rest ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Introduction to Combinatorics, 2nd Edition

Introduction to Combinatorics, 2nd Edition

Martin J. Erickson

Publisher Resources

ISBN: 9781439850527