Transactions of the Cambridge Philosophical Society, المجلد 22University Press, 1923 |
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الصفحة 1
... partitions of a bipartite number ( pq ) and note , as observed long ago by me † , that the partitions are separable into groups which depend upon the partitions of the unipartite numbers ( p ) , ( q ) respectively . Thus the partitions ...
... partitions of a bipartite number ( pq ) and note , as observed long ago by me † , that the partitions are separable into groups which depend upon the partitions of the unipartite numbers ( p ) , ( q ) respectively . Thus the partitions ...
الصفحة 2
... partitions respec- tively the partitions of ( pq ) are separable into PQ groups for every partition of p may be associated with every partition of q . We will now study the enumeration of the partitions appertaining to a given group ...
... partitions respec- tively the partitions of ( pq ) are separable into PQ groups for every partition of p may be associated with every partition of q . We will now study the enumeration of the partitions appertaining to a given group ...
الصفحة 3
... partitions . of the bipartite number ( pq ) which appertain to the group π1 Gr ( pi p2 ... ) , ( q1 × 1 q2X2 ... ) } . To explain this consider the partitions of the bipart ( 33 ) which appertain to the group Gr { ( 21 ) , ( 13 ) ...
... partitions . of the bipartite number ( pq ) which appertain to the group π1 Gr ( pi p2 ... ) , ( q1 × 1 q2X2 ... ) } . To explain this consider the partitions of the bipart ( 33 ) which appertain to the group Gr { ( 21 ) , ( 13 ) ...
الصفحة 4
... partitions of the bipart ( pq ) is in consequence ΣΣ Dm , Day DT ... DΣx hx , hx2 ... h2 , π X וי the double summation being for every partition ( p1 TM 1 p ̧ TM ... .. ) of ( p ) and for every partition ( q1 * 1 q2x2 ... ) of ( q ) ...
... partitions of the bipart ( pq ) is in consequence ΣΣ Dm , Day DT ... DΣx hx , hx2 ... h2 , π X וי the double summation being for every partition ( p1 TM 1 p ̧ TM ... .. ) of ( p ) and for every partition ( q1 * 1 q2x2 ... ) of ( q ) ...
الصفحة 5
... partitions of the bipartite ( 43 ) we take the row commencing 4 and the column headed 3 and find at the intersection the number 57 . The numbers agree with those obtained by expansion of the generating function 1 - ( 1 − x ) ( 1 − y ) ...
... partitions of the bipartite ( 43 ) we take the row commencing 4 and the column headed 3 and find at the intersection the number 57 . The numbers agree with those obtained by expansion of the generating function 1 - ( 1 − x ) ( 1 − y ) ...
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a₁ angle approximately asymptotic expansion atmosphere Axiom of Archimedes axis b₁ c₁ calculated coefficients considered constant convergent convex set cordon corresponding cos² curve d₁ definition denote density determined differential equations disturbance diurnal diurnal variations dyadic earth equal escape expression factor finite follows formula free path function G. H. Hardy giant star given h₂ Hence integral equation invariant Jacobian k₁ k₂ magnitude molecules obtained orbit paper parameters partitions plane positive potential Primitive Roots ratio relation respectively result rotation scalar shew shewn sin² solar solid angle solutions substitution suppose surface t₁ theorem theory v₁ values vector velocity w₁ X₁ XXII zero Σ Σ дх