Narayana Number

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In combinatorics, the Narayana numbers N(n, k), n = 1, 2, 3 ..., 1 ¿ k ¿ n, form a triangle of natural numbers, called Narayana triangle, that occur in various counting problems. They are named for T.V. Narayana, a mathematician from India. Natural numbers have two main purposes: counting ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively. A more recent notion is that of a nominal number, which is used only for naming. Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partition enumeration, are studied in combinatorics.