Some typos and unclear parts found in Ch13
gary317680 opened this issue · comments
Student name: Gary Peng
PID: A15103364
Date of submission: 04/30/2019
Note: corrected parts are bolded if possible
Ch13, p.93
In the third paragraph,
"Every permutation can be uniquely determined by..."
Ch13, p.95
(A)The first paragraph under "13.3 Permutations with Restricted Cycle Strucutre"
The permutation 23154 should have canonical cyclic form (3,1,2)(5,4).
(B)So, under "Lemma 13.1",
"For exmaple, G(23154) = 31254 and G-1(23154) = (2)(3,1)(5,4) = 32154"
***Note: I am unsure if you intended to write a one-line notation for G-1(23154) or perhaps
you intended to say that (2)(3,1)(5,4) and (3,1)(5,4) are equivalent. Are they equivalent?
Ch13, p.96
In "Definition 13.3", it states that "i" is in the set [l-n], but "i" should also be allowed
to be 0, otherwise the subsequence W1,W2,...Wn is not accounted for.
Ch13, p.97
On the side, the URL does not work.
Ch13, p.98
(A)The first paragraph. From the example given, {12345, 23451...}, it seems that the
definition of a 1-cycle class should be "...a subset {p1,...,pn} ⊆Sn such that p_k+1(n) = p_k(1)
and p_k+1(i-1) = p_k(i), for i ∈ {2,3...n}." rather than p_k+1(i+1) = p_k(i).
(B)Then, in the second paragraph:
"Let us now prove that...where C1(p1,...,pk) is equal to the number of completed 1-cycle
classes in p1,...pk." I am unsure about this definition. What does it mean by "completed"
1-cycle classes? Is it different from any 1-cycle classes?
Thank you!
Yes, (2)(3,1)(5,4) and (3,1)(5,4) are equivalent but you are right, it is better to write the permutation in the one line notation.
Thank you for your comments!