Practice Surjective Mapping Proof (21.1.14) - Catalan Numbers - Derivation of Closed Form Formula

Practice: Surjective Mapping Proof

Lesson 21.1.14Catalan Numbers - Derivation of Closed Form Formula

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define a bad sequence in terms of 1s and -1s.
Show hintHide hint
Think about the conditions that need to be met for a sequence to be valid.
Question 2.
What is the binomial coefficient for selecting 2 from 4?
Show hintHide hint
Recall the formula for binomial coefficients C(n, k) = n! / (k!*(n-k)!), where ! denotes factorial.
3Question 3.
What characterizes a surjective mapping?
- Every element in the domain is mapped
- Every element in the codomain is mapped
- Only some elements in the codomain are mapped
Show hintHide hint
Focus on the relationship between domain and codomain.
4Question 4.
True or False: A 'bad' sequence has no negative partial sums at any position.
- True
- False
Show hintHide hint
Go back to the definition of a bad sequence.
Question 5.
Given n = 3, calculate the exact number of valid sequences and explain your methodology.
Show hintHide hint
Break down into steps—first count all, then reflect negative sequences.
Question 6.
If you were to find patterns among valid sequences, describe the fundamental properties that emerge when using reflective methods.
Show hintHide hint
Consider how alterations in each step lead to consistent patterns in counts.

4 more questions in this section. Enroll free to practise them all.