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For all possible values of their arguments, the discrete delta functions  and  , Kronecker delta functions  and  , and signature (Levi–Civita symbol)  are defined by the formulas:
In other words, the Kronecker delta function is equal to 1 if all its arguments are equal.
In the case of one variable, the discrete delta function  coincides with the Kronecker delta function  . In the case of several variables, the discrete delta function  coincides with Kronecker delta function  :
where  is the number of permutations needed to go from the sorted version of  to  .
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