DLMF:26.16.E3 (Q7983): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q12225 / rank
 
Normal rank
Property / Symbols used: Q12225 / qualifier
 
Defining formula:

a j subscript 𝑎 𝑗 {\displaystyle{\displaystyle a_{j}}}

a_{j}
Property / Symbols used: Q12225 / qualifier
 
xml-id: C26.S16.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12226 / rank
 
Normal rank
Property / Symbols used: Q12226 / qualifier
 
Defining formula:

S 𝑆 {\displaystyle{\displaystyle S}}

S
Property / Symbols used: Q12226 / qualifier
 
xml-id: C26.S16.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q12189 / rank
 
Normal rank
Property / Symbols used: Q12189 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q12189 / qualifier
 
xml-id: C26.S9.XMD1.m1bdec

Latest revision as of 14:12, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:26.16.E3
No description defined

    Statements

    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
    DLMF id
    DLMF:26.16.E3
    0 references
    Symbols used
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
    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.m2abdec
    0 references
    Q12216
    Defining formula
    𝔖 n set-of-permutations 𝑛 {\displaystyle{\displaystyle\mathfrak{S}_{\NVar{n}}}}
    xml-id
    C26.S13.p1.m3aadec
    0 references
    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1bdec
    0 references
    Q12225
    Defining formula
    a j subscript 𝑎 𝑗 {\displaystyle{\displaystyle a_{j}}}
    xml-id
    C26.S16.XMD1.m1bdec
    0 references
    Q12226
    Defining formula
    S 𝑆 {\displaystyle{\displaystyle S}}
    xml-id
    C26.S16.XMD2.m1adec
    0 references
    Q12189
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C26.S9.XMD1.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7983&oldid=44628"