2. For a permutation Te Sn, consider = 172...n in one-line notation and let the inversions of T be Inv(T) = {(i, j): 1 Tj}. For example, (1, 4) is an inversion of 35412, since the first entry in 35412 (3) is larger than the fourth entry (1). In total, Inv(35412) = {(1,4), (1,5), (2, 3), (2, 4), (2, 5), (3, 4), (3,5)}, so 35412 has 7 inversions. (a) How many inversions are in the permutation 2437165? (b) What is the maximum possible number of inversions for a permutation in Sn?
2. For a permutation Te Sn, consider = 172...n in one-line notation and let the inversions of T be Inv(T) = {(i, j): 1 Tj}. For example, (1, 4) is an inversion of 35412, since the first entry in 35412 (3) is larger than the fourth entry (1). In total, Inv(35412) = {(1,4), (1,5), (2, 3), (2, 4), (2, 5), (3, 4), (3,5)}, so 35412 has 7 inversions. (a) How many inversions are in the permutation 2437165? (b) What is the maximum possible number of inversions for a permutation in Sn?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
#2
Transcribed Image Text:2. For a permutation T E Sn, consider T = T1T2 ...Tn in one-line notation and let the inversions of T be
Inv(T) = {(i, j): 1<i<j<n and Ti > Tj}.
For example, (1, 4) is an inversion of 35412, since the first entry in 35412 (3) is larger than the fourth
entry (1). In total, Inv (35412) = {(1,4), (1, 5), (2, 3), (2, 4), (2,5), (3, 4), (3,5)}, so 35412 has 7 inversions.
(a) How many inversions are in the permutation 2437165?
(b) What is the maximum possible number of inversions for a permutation in Sn?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
