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2012•International Journal of Computer ApplicationsRequires access

An Algorithm to Count onto Functions

Rinku Kumar, Rakesh Kamboj, Chetan Pahwa

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Abstract

paper proposes an algorithm to derive a general formula to count the total number of onto functions feasible from a set A with cardinality n to a set B with cardinality m. Let f:A→B is a function such that │A│=n and │B│=m, where A and B are finite and non-empty sets, n and m are finite integer values. To count the total number of onto functions feasible till now we have to design all of the feasible mappings in an onto manner, this paper will help in counting the same without designing all possible mappings and will provide the direct count on onto functions using the formula derived in it.

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What this paper is about

paper proposes an algorithm to derive a general formula to count the total number of onto functions feasible from a set A with cardinality n to a set B with cardinality m. Let f:A→B is a function such that │A│=n and │B│=m, where A and B are finite and non-empty sets, n and m are finite integer values. To count the total number of onto functions feasible till now we have to design all of the feasible mappings in an onto manner, this paper will help in counting the same without designing all possible mappings and will provide the direct count on onto functions using the formula derived in it.

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Available abstract

paper proposes an algorithm to derive a general formula to count the total number of onto functions feasible from a set A with cardinality n to a set B with cardinality m. Let f:A→B is a function such that │A│=n and │B│=m, where A and B are finite and non-empty sets, n and m are finite integer values. To count the total number of onto functions feasible till now we have to design all of the feasible mappings in an onto manner, this paper will help in counting the same without designing all possible mappings and will provide the direct count on onto functions using the formula derived in it.

Key concepts: Cardinality (data modeling), Set (abstract data type), Integer (computer science), Computer science, Function (biology), Finite set, Algorithm, Cardinal number (linguistics)

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