Question

Consider the set Pn of all partitions of the set [n] into non-empty blocks, that is:...

Consider the set Pn of all partitions of the set [n] into non-empty blocks, that is:

Pn = {π | π is a set partition of [n]}

  1. Prove that this is a poset

Homework Answers

Answer #1

oi

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let A be a non-empty set. Prove that if ∼ defines an equivalence relation on the...
Let A be a non-empty set. Prove that if ∼ defines an equivalence relation on the set A, then the set of equivalence classes of ∼ form a partition of A.
Let X be a non-empty finite set with |X| = n. Prove that the number of...
Let X be a non-empty finite set with |X| = n. Prove that the number of surjections from X to Y = {1, 2} is (2)^n− 2.
Proposition 16.4 Let S be a non–empty finite set. (a) There is a unique n 2...
Proposition 16.4 Let S be a non–empty finite set. (a) There is a unique n 2 N1 such that there is a 1–1 correspondence from {1, 2,...,n} to S. We write |S| = n. Also, we write |;| = 0. (b) If B is a set and f : B ! S is a 1–1 correspondence, then B is finite and |B| = |S|. (c) If T is a proper subset of S, then T is finite and |T| <...
Let A be a non-empty set and f: A ? A be a function. (a) Prove...
Let A be a non-empty set and f: A ? A be a function. (a) Prove that, if f is injective but not surjective (which means that the set A is infinite), then f has at least two different left inverses.
Is empty set a proper subset of a non-empty set? Why or why not?
Is empty set a proper subset of a non-empty set? Why or why not?
For n > 0, let an be the number of partitions of n such that every...
For n > 0, let an be the number of partitions of n such that every part appears at most twice, and let bn be the number of partitions of n such that no part is divisible by 3. Set a0 = b0 = 1. Show that an = bn for all n.
Let V = Pn(R), the vector space of all polynomials of degree at most n. And...
Let V = Pn(R), the vector space of all polynomials of degree at most n. And let T : V → V be a linear transformation. Prove that there exists a non-zero linear transformation S : V → V such that T ◦ S = 0 (that is, T(S(v)) = 0 for all v ∈ V) if and only if there exists a non-zero vector v ∈ V such that T(v) = 0. Hint: For the backwards direction, consider building...
. Prove that, for all integers n ≥ 1, Pn i=1 i(i!) = (n + 1)!...
. Prove that, for all integers n ≥ 1, Pn i=1 i(i!) = (n + 1)! − 1
For what n do there exist self-conjugate partitions of n all of whose parts are even?
For what n do there exist self-conjugate partitions of n all of whose parts are even?
Finding the Mean The mean (or average) of a non-empty list of n numbers is the...
Finding the Mean The mean (or average) of a non-empty list of n numbers is the sum of the numbers divided by n. For example, the mean of 2, 7, 3, 9, and 13 is (2+7+3+9+13)/5, or 6.8. Write a function mean that takes as input a non-empty list of numbers (of any length > 0) and returns the mean.