038-2015

MO640 - Multiple-choice question

Let α be a 3-cycle and β be an arbitrary permutation. If two of the elements a, b of α are in the same cycle of β and the third element c is in another cycle of β, we have the following changes from β to the composition αβ :

1. The cycle of β with a and b breaks into two new cycles. The cycle with c remains the same.
2. The cycle with c breaks into two new cycles. The cycle with a and b recombines into a different cycle.
3. These two cycles of β join together into a new cycle.
4. These two cycles of β recombine into two new cycles.
5. None of the above.

Original idea by: Juan Felipe Hernández Albarracín.

037-2015

MO640 - Multiple-choice question

Consider the following genome with seven synteny blocks:

The correct representation π_chr for this genome according to the chromosomal model is:

A) (C -B A -A B -C) (F G) (-G -F) (D -E E -D)
B) (A C -B B -C -A) (-F G) (-G F) (D E -E -D)
C) (-A C -B B -C A) (F G) (-F -G) (-E D -D E)
D) (B A C -C -A -B) (G F) (-F -G) (-E D -D E)
E) None of the above.

Original idea by: Celso A. W. Santos

051-2004

MO640 - Multiple-choice question

Consider the following permutation and choose the right answer:

a) The support of this permutation is {4,5,6}.
b) The breakdown of this permutation in pairwise disjoint cycles produces exactly three cycles with lenght greater than 1.
c) The breakdown of this permutation in pairwise disjoint cycles can be represented as (173)(298).
d) The permutation is a 6-cycle.
e) None of above.

Original idea by: José Augusto Amgarten Quitzau
Translation help by: Andrey Victor Justo

025-2011

MO640 - Multiple-choice question

Among the statements below, choose the INCORRECT one.

a) Given a permutation α, its inverse α^-1 is obtained by inverting the order of elements in each cycle of the cycle decomposition of α.
b) Let α = (a b) and β be any permutation. If a and b are in the same cycle in the cycle decomposition of β, then this cycle will be partitioned into two in the cycle decomposition of αβ.
c) Let α = (a b) and β be any permutation. If a and b are in separate cycles in the cycle decomposition of β, these cycles will turn into a single cycle in the cycle decomposition of αβ.
d) Let α = (a b c) and β be a permutation in which a, b, and c are distributed over two distinct cycles.  The total number of cycles in αβ will be less than the total number of cycles in β.
e) None of the above.

Translated by: Raphael Cristofaro
Original idea by: Kaio Karam

036-2015

MO640 - Multiple-choice question

Which sentence is false?

Figure 1

          

                Figure 2

     

     Figure 3

a. The cycle notation for the permutation in Figure 1 is β = (1 5 4 3 2).
b. The cycle notation for the permutation in Figure 2 is α = (1 2 3 4 5).
c. The permutation in Figure 1 is the inverse of the permutation in Figure 3.
d. The permutations in Figures 2 and 3 commute.
e. None of the above

Original idea by: Jéssica Akemi Matsuoka

035-2015

MO640 - Multiple-choice question

The set {1,2,3,...,10} is partitioned in how many orbits by the permutation below?

a) 2
b) 4
c) 5
d) 8
e) None of the above

Original idea by: Leandro Tacioli

056-2007

MO640 - Multiple-choice question

Given that α = (a b), β = (a b c d), and γ = (a c)(b d), chose the FALSE alternative:

1. αβ = (a)(b c d);
2. βα = (a c d)(b); 
3. αγ = (a c d b); 
4. γα = (a d b c); 
5. NDA 

Original idea by: Moacy Barros Correia da Silva
Translation help by : Rafael S. Padilha