wˌɛɹ ɪz ðə sˈaɪn fˈʌŋkʃən ʌv pˌɜːmjuːtˈeɪʃənz ɪnðə pˌɜːmjuːtˈeɪʃən ɡɹˈuːp , wˌɪtʃ ɹᵻtˈɜːnz ænd fɔːɹ ˈiːvən ænd ˈɑːd pˌɜːmjuːtˈeɪʃənz, ɹᵻspˈɛktɪvli.
where  is the sign function of permutations in the permutation group , which returns  and  for even and odd permutations, respectively.