The Catalan Numbers C_n Count the Number of Strings of N

question 68

Short Answer

The Catalan numbers C_n count the number of strings of n +’s and n −’s with the following property: as each string is read from left to right, the number of +’s encountered is always at least as large as the number
of −’s.
(a) Verify this by listing these strings of lengths 2, 4, and 6 and showing that there are C₁ , C₂ , and C₃ of
these, respectively.
(b) Explain how counting these strings is the same as counting the number of ways to correctly parenthesize
strings of variables

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Definitions:

Money Supply Growth Rate

The rate at which the amount of money available in an economy is growing, influencing inflation and economic stability.

Phillips Curve

A concept suggesting an inverse relationship between the rate of inflation and the rate of unemployment within an economy.

Desired Expenditures

The amount of spending households, firms, and the government wish to make, usually influenced by economic conditions and policies.

Inflation

A persistent upsurge in the average cost of goods and services across an economy over time.