DLMF:26.16.E2 (Q7982): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12216 / rank
 
Normal rank
Property / Symbols used: Q12216 / qualifier
 
Defining formula:

𝔖 n set-of-permutations 𝑛 {\displaystyle{\displaystyle\mathfrak{S}_{\NVar{n}}}}

\npermutations{\NVar{n}}
Property / Symbols used: Q12216 / qualifier
 
xml-id: C26.S13.p1.m3adec

Revision as of 14:12, 2 January 2020

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DLMF:26.16.E2
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    Statements

    Defining formula
    ∑ σ ∈ 𝔖 S q inv ( σ ) = [ a 1 + a 2 + ⋯ + a n a 1 , a 2 , … , a n ] q , subscript 𝜎 set-of-permutations 𝑆 superscript 𝑞 inv 𝜎 q-multinomial subscript 𝑎 1 subscript 𝑎 2 ⋯ subscript 𝑎 𝑛 subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑛 𝑞 {\displaystyle{\displaystyle\sum_{\sigma\in\mathfrak{S}_{S}}q^{\mathop{\mathrm% {inv}}(\sigma)}=\genfrac{[}{]}{0.0pt}{}{a_{1}+a_{2}+\cdots+a_{n}}{a_{1},a_{2},% \ldots,a_{n}}_{q},}}
    0 references
    DLMF id
    DLMF:26.16.E2
    0 references
    Symbols used
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
    Q12224
    Defining formula
    [ a 1 + a 2 + … + a n a 1 , a 2 , … , a n ] q q-multinomial subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑛 subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑛 𝑞 {\displaystyle{\displaystyle\genfrac{[}{]}{0.0pt}{}{\NVar{a_{1}}+\NVar{a_{2}}+% \dots+\NVar{a_{n}}}{\NVar{a_{1}},\NVar{a_{2}},\ldots,\NVar{a_{n}}}_{\NVar{q}}}}
    xml-id
    C26.S16.p3.m2aadec
    0 references
    Q12216
    Defining formula
    𝔖 n set-of-permutations 𝑛 {\displaystyle{\displaystyle\mathfrak{S}_{\NVar{n}}}}
    xml-id
    C26.S13.p1.m3adec
    0 references
     
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