The Catalan Numbers $C _ { n }$ Count the Number of Strings of N +’S and Number

question 89

Essay

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:

Correct Actions

Appropriate or effective measures taken to achieve a desired outcome or resolve a specific situation.

Monopsony

A market situation where there is only one buyer for a product or service.

Labor Market

The supply of available workers in relation to available work.

Labor Supply Curve

A graphical representation showcasing the relationship between the wage rate and the quantity of labor workers are willing to supply.