By way of collecting a short-term pay-off for all the work — not to mention all the peirce-spiration — that we sweated out over the regular representations of the Klein 4-group <math>V_4,\!</math> let us write out as quickly as possible in ''relative form'' a minimal budget of representations of the symmetric group on three letters, <math>S_3 = \operatorname{Sym}(3).</math> After doing the usual bit of compare and contrast among these divers representations, we will have enough concrete material beneath our abstract belts to tackle a few of the presently obscur'd details of Peirce's early "Algebra + Logic" papers. | By way of collecting a short-term pay-off for all the work — not to mention all the peirce-spiration — that we sweated out over the regular representations of the Klein 4-group <math>V_4,\!</math> let us write out as quickly as possible in ''relative form'' a minimal budget of representations of the symmetric group on three letters, <math>S_3 = \operatorname{Sym}(3).</math> After doing the usual bit of compare and contrast among these divers representations, we will have enough concrete material beneath our abstract belts to tackle a few of the presently obscur'd details of Peirce's early "Algebra + Logic" papers. |