especies combinatóries: parts dos

[ m·( {a_{i_{k}},a_{j_{k}}} ) ]


∑ ( ( m·[ k // 2 ] )·x^{k} )


[ m·( {a_{i_{k}},a_{j_{k}}} ) ] + [ n·( {a_{i_{k}},a_{j_{k}}} ) ] = ...
... [ (m+n)·( {a_{i_{k}},a_{j_{k}}} ) ]


∑ ( ( (m+n)·[ k // 2 ] )·x^{k} )


[ m·( {a_{i_{k}},a_{j_{k}}} ) ] [x] [ n·( {a_{i_{k}},a_{j_{k}}} ) ] = ...
... [ (m·n)·( {a_{i_{k}},a_{j_{k}}} [x] {a_{i_{k}},a_{j_{k}}} ) ]


∑ ( ( (m·n)·[ k // 2 ]^{2} )·x^{k} )

especies combinatóries

[ n·( {a_{k},a_{1},a_{2}},...,{a_{k+(-1)},a_{k},a_{1}} ) ]


∑ ( ( n·k )·x^{k} )


[ m·( {a_{k},a_{1},a_{2}},...,{a_{k+(-1)},a_{k},a_{1}} ) ]+...
... [ n·( {a_{k},a_{1},a_{2}},...,{a_{k+(-1)},a_{k},a_{1}} ) ] = ...
... [ (m+n)·( {a_{k},a_{1},a_{2}},...,{a_{k+(-1)},a_{k},a_{1}} ) ]


∑ ( ( (m+n)·k )·x^{k} )
 
f: [n·( {a_{1}},...,{a_{k}} )] ---> [ n·( {a_{k},a_{1},a_{2}},...,{a_{k+(-1)},a_{k},a_{1}} ) ] és bijectiva.


f({a_{j}}) = {a_{j+(-1)},a_{j},a_{j+1}} = {a_{i+(-1),a_{i},a_{i+1}}} = f({a_{i}})
j+(-1) = i+(-1) & j+1 = i+1
j=i

especies combinatóries

[ n·( {a_{k},a_{2}},...,{a_{k+(-1)},a_{1}} ) ]


∑ ( ( n·k )·x^{k} )


[ m·( {a_{k},a_{2}},...,{a_{k+(-1)},a_{1}} ) ]+[ n·( {a_{k},a_{2}},...,{a_{k+(-1)},a_{1}} ) ] = ...
... [ (m+n)·( {a_{k},a_{2}},...,{a_{k+(-1)},a_{1}} ) ]


∑ ( ( (m+n)·k )·x^{k} )
 
f: [n·( {a_{1}},...,{a_{k}} )] ---> [ n·( {a_{k},a_{2}},...,{a_{k+(-1)},a_{1}} ) ] és bijectiva.


f({a_{j}}) = {a_{j+(-1)},a_{j+1}} = {a_{i+(-1),a_{i+1}}} = f({a_{i}})
j+(-1) = i+(-1) & j+1 = i+1
j=i

especies combinatóries: el octopus

[ A_{1},...,A_{j} ]-[ m·( {a_{1}},...,{a_{k}} ) ]


∑ (m·k+j)·x^{k}


[ A_{1},...,A_{j} ]-[ m·( {a_{1}},...,{a_{k}} ) ] + [ B_{1},...,B_{s} ]-[ n·( {a_{1}},...,{a_{k}} ) ] = ...
... [ A_{1},...,A_{j},B_{1},...,B_{s} ]-[ (m+n)·( {a_{1}},...,{a_{k}} ) ]


∑ ( (m+n)·k+(j+s) )·x^{k}


[ A_{1},...,A_{j} ]-[ m·( {a_{1}},...,{a_{k}} ) ] [x] [ B_{1},...,B_{s} ]-[ n·( {a_{1}},...,{a_{k}} ) ] = ...
... [ A_{j} [x] B_{s} ]-[ (ms+nj)·( {a_{1}},...,{a_{k}} ) ]-[ (m·n)·( {a_{k}} [x] {a_{k}} ) ]


∑ ( (m·n)·k^{2}+(ms+nj)·k+(j·s) )·x^{k}

especies combinatóries

[ n·( {a_{1}},...,{a_{k}} ) ]


∑ ( ( n·k )·x^{k} )


[ m·( {a_{1}},...,{a_{k}} ) ] + [ n·( {a_{1}},...,{a_{k}} ) ] = [ (m+n)·( {a_{1}},...,{a_{k}} ) ]


∑ ( ( (m+n)·k )·x^{k} )


[ m·( {a_{1}},...,{a_{k}} ) ] [x] [ n·( {a_{1}},...,{a_{k}} ) ] = ...
... [ (m·n)·( {a_{k}} [x] {a_{k}} ) ]


∑ ( ( (m·n)·k^{2} )·x^{k} )

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index de etiquetes matemàtiques