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DLMF:26.16.E3 - MaRDI portal

DLMF:26.16.E3 (Q8676)

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DLMF:26.16.E3
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    Statements

    DLMF defining formula
    ∑ σ ∈ 𝔖 S q maj ( σ ) = [ a 1 + a 2 + ⋯ + a n a 1 , a 2 , … , a n ] q . subscript 𝜎 set-of-permutations 𝑆 superscript 𝑞 maj 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% {maj}}(\sigma)}=\genfrac{[}{]}{0.0pt}{}{a_{1}+a_{2}+\cdots+a_{n}}{a_{1},a_{2},% \ldots,a_{n}}_{q}.}}
    0 references
    Symbols used
    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
    0 references
    Q12227
    DLMF 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.m2abdec
    0 references
    set of permutations of { 1 , 2 , … , n }
    DLMF defining formula
    𝔖 n set-of-permutations 𝑛 {\displaystyle{\displaystyle\mathfrak{S}_{\NVar{n}}}}
    xml-id
    C26.S13.p1.m3aadec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1bdec
    0 references
    numbers
    DLMF defining formula
    a j subscript 𝑎 𝑗 {\displaystyle{\displaystyle a_{j}}}
    xml-id
    C26.S16.XMD1.m1bdec
    0 references
    multiset
    DLMF defining formula
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C26.S16.XMD2.m1adec
    0 references
    parameter
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C26.S9.XMD1.m1bdec
    0 references

    Identifiers

     
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