Signature[{Subscript[n, 1], Subscript[n, 2], \[Ellipsis], Subscript[n, d]}] == -Signature[{Subscript[n, 2], Subscript[n, 1], \[Ellipsis], Subscript[n, d]}]

Cell[BoxData[RowBox[List[RowBox[List["Signature", "[", RowBox[List["{", RowBox[List[SubscriptBox["n", "1"], ",", SubscriptBox["n", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["n", "d"]]], "}"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List["Signature", "[", RowBox[List["{", RowBox[List[SubscriptBox["n", "2"], ",", SubscriptBox["n", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["n", "d"]]], "}"]], "]"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msub> <mi> &#949; </mi> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mtext> </mtext> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mtext> </mtext> <mo> , </mo> <mtext> </mtext> <msub> <mi> n </mi> <mi> d </mi> </msub> </mrow> </msub> <mo> &#10869; </mo> <mrow> <mo> - </mo> <msub> <mi> &#949; </mi> <mrow> <msub> <mi> n </mi> <mn> 2 </mn> </msub> <mo> , </mo> <mtext> </mtext> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> , </mo> <mo> &#8230; </mo> <mtext> </mtext> <mo> , </mo> <mtext> </mtext> <msub> <mi> n </mi> <mi> d </mi> </msub> </mrow> </msub> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Signature </ci> <list> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> d </ci> </apply> </list> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Signature </ci> <list> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> d </ci> </apply> </list> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Signature", "[", RowBox[List["{", RowBox[List[SubscriptBox["n_", "1"], ",", SubscriptBox["n_", "2"], ",", "\[Ellipsis]_", ",", SubscriptBox["n_", "d_"]]], "}"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", RowBox[List["Signature", "[", RowBox[List["{", RowBox[List[SubscriptBox["nn", "2"], ",", SubscriptBox["nn", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["nn", "d"]]], "}"]], "]"]]]]]]]]

2001-10-29