Transactions of the Cambridge Philosophical Society, المجلد 22University Press, 1923 |
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الصفحة 1
... shewn that the actual denumeration may be made to depend upon the theory of the symmetric functions of a single system of quantities . Such a system is and I write in the usual notation A1 , A2 , A3 , ... ) ( 1 − α1x ) ( 1 − α2x ) ( 1 ...
... shewn that the actual denumeration may be made to depend upon the theory of the symmetric functions of a single system of quantities . Such a system is and I write in the usual notation A1 , A2 , A3 , ... ) ( 1 − α1x ) ( 1 − α2x ) ( 1 ...
الصفحة 3
... shewn ( loc . cit . ) to have either of the two expressions Dm , Dm , ... Dex hx1 h x2 ... h2 = 1 DX1 Dx2 ΧΙ X1 Dεx hx2 ... Dε h2 h2 ... 2 hex⋅ The expressions are equivalent and may be evaluated by means 1-2 MAJOR MACMAHON , ON ...
... shewn ( loc . cit . ) to have either of the two expressions Dm , Dm , ... Dex hx1 h x2 ... h2 = 1 DX1 Dx2 ΧΙ X1 Dεx hx2 ... Dε h2 h2 ... 2 hex⋅ The expressions are equivalent and may be evaluated by means 1-2 MAJOR MACMAHON , ON ...
الصفحة 4
... shews hgh , ... +7 ( 21 ) + ... D2 Dhah , 27 . The above resulting numbers are all shewn in the Tables which proceed as far as the weight 6 . In the above case where p = q , it is not necessary to consider all the groups because the two ...
... shews hgh , ... +7 ( 21 ) + ... D2 Dhah , 27 . The above resulting numbers are all shewn in the Tables which proceed as far as the weight 6 . In the above case where p = q , it is not necessary to consider all the groups because the two ...
الصفحة 6
... shewing that there are 7 partitions into 4 or fewer parts ; in addition to the 2 which have exactly 3 parts already written down we have 5 which contain exactly 4 parts ; these are ( 22 , 11 , 10 , 01 ) , ( 21 , 12 , 10 , 01 ) , ( 21 ...
... shewing that there are 7 partitions into 4 or fewer parts ; in addition to the 2 which have exactly 3 parts already written down we have 5 which contain exactly 4 parts ; these are ( 22 , 11 , 10 , 01 ) , ( 21 , 12 , 10 , 01 ) , ( 21 ...
الصفحة 8
... extend to Ex and ... AΣπ - Ex + 5 X1 azπ - 2x + 3 ( x + 1 ) terms , whilst if Ex be even Ex - 1 terms respectively . That these two series are equivalent may be shewn algebraically 8 MAJOR MACMAHON , ON COMPOUND DENUMERATION .
... extend to Ex and ... AΣπ - Ex + 5 X1 azπ - 2x + 3 ( x + 1 ) terms , whilst if Ex be even Ex - 1 terms respectively . That these two series are equivalent may be shewn algebraically 8 MAJOR MACMAHON , ON COMPOUND DENUMERATION .
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