questions regarding the re-orderings of some finite set of objects.
1
vote
2answers
23 views
Inclusion & Exclusion: In how many permutations of the digits $0,…,9$ there's no continuity of 7 digits or more?
In how many permutations of the digits $0,...,9$ there's no continuity of 7 digits or more?
(Ex. the number 203456789 1 should not be counted)
I believe that the basic case, for the inclusion ...
4
votes
1answer
46 views
Calculating the sign of the generalised permutation
What is the sign of the following permutation. Prove your answer:
$$\pmatrix{1 & 2 & \cdots&p&p+1&\cdots & \cdots &p+q \\ q+1 & \cdots & \cdots & q + ...
1
vote
0answers
15 views
Bit permutations and collisions of compression function
I'm having trouble finding a good method for solving the following problem:
If $n$ is a positive integer, let $S_n$ denote the group of permutations of the set $\{1,2,\dots, n\}$. For a permutation ...
0
votes
1answer
24 views
Listing the elements of $A(3)$
List the elements of $A(3)$ and give the order of each of them.
This is about permutations in number theory ... to clarify that $A(n)$
Thanks!
1
vote
2answers
29 views
Finding the sign of each permutations
How to find the sign of each of the following permutations?
1, (1 2 3 4 5)(8 7 6)(10 11)
2, (1 3 5 7 9 11)(2 4 6 8 10)
3, (1 2)(3 4)(5 6 7 8)(9 10)
4, (1 2 3 4 5 6 7 8)(1 8 7 6 5 4 3 2)
Help ...
0
votes
1answer
17 views
Explanation on step $\rho$ of the SHA-3 algorithm
I'm working on implementing SHA-3 in a PIC microcontroller.
In the block permutation, I don't quite understand step $\rho$:
Bitwise rotate each of the 25 words by a different triangular number 0, ...
2
votes
1answer
39 views
Any comprehensive material to revise the mathematics
I left school long back and so my mathematics knowledge also fades out.
I am trying hard to re-collect the basics about log / permutaion / combination / probability / polynomial equations.
I tried ...
1
vote
3answers
23 views
this can be solved bypermutation and combination based problem
How many three are there whose hundred digit is greater than tens digit which in turn is greater than the unit digit?
Ans:I tried it But couldn't solve..
5
votes
1answer
57 views
Combinations and group theory
First question. I'm just generally curious about combinations in group theory. How do they relate?
If I take the set of permutations of <1,2,3,4>, I get the symmetry group S4. How about the set ...
0
votes
0answers
32 views
Placing red and black balls in n places
There are n places and there are c1 number of black balls with each numbered from 1 to c1 and ...
2
votes
3answers
54 views
Odd/Even Permutations
How do you classify a permutation as odd or even (composition of an odd or even number of transpositions)? I somewhat understand the textbook definition of it but im having hard time conceptualizing ...
0
votes
1answer
34 views
Permuation with repeated letters and consecutive letters not same
I have been trying to solve a question on permutation and haven't really been successful. I want to generate all the permutations of a specified length that start with a letter and end with the ...
3
votes
4answers
83 views
Is my textbook wrong?
My textbook says (without explaining how it is done):
$$\begin{pmatrix}
1\ 2\ 3\ 4\\
2\ 1\ 4\ 3
\end{pmatrix}\begin{pmatrix}
1\ 2\ 3\ 4\\
2\ 3\ 4\ 1
\end{pmatrix}=\begin{pmatrix}
1\ ...
2
votes
2answers
114 views
+50
Dihedral group and cyclic group theorem.
Let $D_n$ be the dihedral group defined by $D_n=$ {$I,R,R^2,...,R^{(n−1)},r,rR,rR^2,...rR^{(n−1)}$}
Theorem. A nontrivial proper subgroup $N$ of $D_n$ is normal in $D_n$ if and only if $N$ is a ...
0
votes
1answer
45 views
number of ways of placing balls on plate
There are n plates places in a line and unlimited number of red balls with values from 1 to ...
