In mathematics, a combinatorial explosion is the rapid growth of the complexity of a problem due to how the combinatorics of the problem is affected by the input, constraints, and bounds of the problem. Combinatorial explosion is sometimes used to justify the intractability of certain problems. Examples of such problems include certain mathematical functions, the analysis of some puzzles and games, and some pathological examples which can be modelled as the Ackermann function.
Examples
Latin squares
A Latin square of order n is an n × n array with entries from a set of n elements with the property that each element of the set occurs exactly once in each row and each column of the array. An example of a Latin square of order three is given by,
A common example of a Latin square would be a completed Sudoku puzzle. A Latin square is a combinatorial object (as opposed to an algebraic object) since only the arrangement of entries matters and not what the entries actually are. The number of Latin squares as a function...