Proving the Number of SDRs in a Collection of Sets: A Mathematical Analysis

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In summary, the conversation is discussing the number of SDRs (System of Distinct Representatives) in a collection of sets. The first part of the conversation mentions a collection with n+1 sets, each containing 2, 3, ..., n+1 elements respectively, and the question is to show that this collection has at least 2^n SDRs. The second part provides equations for calculating the number of SDRs, with k representing the number of elements in a set and n being a constant. The third part clarifies the values of k and n in the equations and suggests that in order to have exactly 2^n SDRs, each set in the collection must have 2 new elements not present in
  • #1
junho
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1. Suppose A1,A2,...,An contain 2,3,...,n+1 elements, respectively. Show that this collection has at least 2^n SDRs. Find such a collection with exactly 2^n SDRs



2. These are the only equations given in my notes regarding "the number of SDRs a collection of sets has"
k! if k <= n
k!/(k-n)! if k > n




3. Ok, for part one of the question, I know that I have to show that k! > 2^n. I can't seem to decide what k is in this case, is k = 2? or is k variable for each set within the collection?

And for part 2, I'm just doing my best to guess, but to have exactly 2^n SDR's I think that each successive set in the collection must have 2 elements that don't exist in the previous set. Is my line of thinking correct?

Thank you in advance for any help.
 
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  • #2
It might be helpful if you would define "DR" and "SDR" here.
 
  • #3
HallsofIvy said:
It might be helpful if you would define "DR" and "SDR" here.

Sorry. I'll do just that.

First of all, DR was a typo.
SDR = System of Distinct Representatives
 

FAQ: Proving the Number of SDRs in a Collection of Sets: A Mathematical Analysis

What is an SDR?

An SDR, or Special Drawing Rights, is an international reserve asset created by the International Monetary Fund (IMF) to supplement the existing official reserves of member countries.

How are SDRs used?

SDRs can be used as a unit of account, a medium of exchange, or a store of value. They are primarily used by central banks and international organizations to settle international debts and conduct transactions.

How are SDRs valued?

The value of an SDR is based on a basket of major currencies: the US dollar, euro, Chinese yuan, Japanese yen, and British pound. The IMF reviews and adjusts the valuation every five years to reflect changes in the global economy.

Who can use SDRs?

Only member countries of the IMF can hold and use SDRs. As of 2021, there are 190 member countries.

What are the benefits of SDRs?

SDRs provide a stable and diversified reserve asset for countries, reducing their reliance on any single currency. They also promote international monetary cooperation and can help stabilize the global financial system.

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