Number theorySince the 18th century the theory of partitions has interested some of the best minds. While it seems to have little or no practical application, it has, in a certain sense, just the right degree of difficulty. The problems are far from trivial, but at the same time they ...
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partitionstheorymodinfinitelysinhintegers Thetheoryofpartitions n=n 1 +n 2 +…+n i 7=3+2+2 7=4+2+1 55113++++ 5 2+ 3+ 3+ 2+ p(n)=thenumberofpartitionsofn p(1)=11 p(2)=22,1+1 p(3)=33,2+1,1+1+1 p(4)=54,3+1,2+2,2+1+1,1+1+1+1 p(5)=75,4+1,3+2,3...
The work of the Indian mathematician, Srinivasa Ramanujan(c.1887), has laid a basis for those interested in the theory of partitions. In 1966, two computational number theorists, Thomas Parkin and Daniel Shanks, wrote a paper on the parity of the partition function and supported their results ...
CHAPTER 21 – Classifying Spaces of Compact Lie Groups and Finite Loop Spaces This chapter deals with the explanation of classifying spaces of compact lie groups and finite loop spaces. The basic problem of the homotopy theory is to classify spaces and maps between spaces up to homotopy by means...
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the Mathematical and Physical Section of the British Association a Exeter, the Nugae Mathematicae, Sylvester's enumerative method of obtaining the complete system of concomitants of a system of quantics, his constructive theory of partitions, binary matrices, and lectures on the theory of reciproc...
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Results on the existence, improvement, and the shrinking of perfect resolutions are established.Bibliography: 11 titles. 关键词: random hypergraph Vapnik-Chervonenkis testing dimension threshold DOI: 10.1070/SM2007v198n07ABEH003866 被引量: 11 年份: 2007 ...
The function is defined as the number of partitions of the integer n into exactly m nonzero positive integers where the order is irrelevant. A series in which the leading terms alternate in sign is given for which yields good numerical estimates. DOI: 10.1090/S0025-5718-1982-0658226-5 年份...