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A general asymptotic formula for partition functions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Brigham, Nelson A. |
| Copyright Year | 1950 |
| Abstract | ()a n (n)[y(n) +1]* [y(n) + kn -1J (3 ) = E k=-1k+2k+-k. . ,kZ,k$O n1 kni Thus the partition k = lki+2k2+ +Ikt of k into ki ones, k2 twos, and so on, is weighted in a certain way by the product shown, and various partition functions are obtained by choosing the function 'y(n) appropriately. For example, if 'y(n) =1 for all n, then ay(k) becomes the unrestricted partition function; if 'y(n) = n for all n, then a,,(k) becomes the plane partition of Wright [2];' if 'y(n) =1 for rth powers and 0 otherwise, then a.,(k) is the number of partitions of k into rth powers; and so on. The purpose of this paper is to establish the asymptotic formula |
| Starting Page | 182 |
| Ending Page | 191 |
| Page Count | 10 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-1950-0034409-3 |
| Volume Number | 1 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/1950-001-02/S0002-9939-1950-0034409-3/S0002-9939-1950-0034409-3.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-1950-0034409-3 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
