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The van Rhijn function is a basic datum for the local portion of the Galaxy, but it is not necessarily representative for an area larger than the immediate solar neighbourhood.
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Hence ((texttt {A}_{theta, j},rho )) is a basic datum.
Hence ((texttt {B}_{theta, j},rho )) is a basic datum.
Let ((mathcal {X}, rho )) be a basic datum and let (mathcal {R}= (mathcal {C}, varDelta )) and (mathcal {R}' = mathcal {R}(mathcal {C}, varDelta ')) be two generalized root systems for ((mathcal {X}, rho )) with the same bundle (mathcal {C}).
This is a basic step for reformatting.
That's a basic thing for me.
Let (mathcal {R}= (mathcal {X}, rho )) be a connected basic datum of size (mathbb {I}= mathbb {I}_{theta }).
Let now (mathcal {R}= (mathcal {C}, varDelta )) be an arithmetic root system over a basic datum ((mathcal {X}, rho )).
By the axioms above, (mathbf {M} = (mathbf {m} ^x)_{xin mathcal {X}}) is a Coxeter datum for ((mathcal {X}, rho )).
A Coxeter groupoid over a basic datum of size one is just a Coxeter group.
All the combinatorial structures in this context are sorts of bundles over a basis with prescribed changes, that we formally call a basic datum.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com