| 词条 | Frank Garvan |
| 释义 |
Francis G. Garvan (born March 9, 1955) is an Australian-born mathematician who specializes in number theory and combinatorics. He holds the position Professor of Mathematics at the University of Florida.[1] He received his Ph.D. from Pennsylvania State University (January, 1986) with George E. Andrews as his thesis advisor.[2] Garvan's thesis, Generalizations of Dyson's rank, concerned the rank of a partition[3] and formed the groundwork for several of his later papers[4]. Garvan is well-known for his work in the fields of q-series and integer partitions. Most famously, in 1988 Garvan and Andrews discovered a definition of the crank of a partition[5]. The crank of a partition is an elusive combinatorial statistic similar to the rank of a partition which provides a key to the study of Ramanujan congruences in partition theory. It was first described by Freeman Dyson in a paper on ranks for the journal Eureka in 1944[6]. Andrews and Garvan's definition was the first defintion of a crank to satisfy the properties hypothesized for it in Dyson's paper. References1. ^ , retrieved 2016-01-26. 2. ^[https://www.math.rutgers.edu/~asills/geastudents.html], retrieved 2016-01-26. 3. ^ {{cite thesis |last=Garvan |first=Francis G. |date=May 1986 |title=Generalizations of Dyson's rank |type= |chapter=1 |publisher= |docket= |oclc= |url=http://qseries.org/fgarvan/phd-thesis/index.html |access-date=2019-03-22}} 4. ^{{cite web |last1=Garvan |first1=Francis G. |title=Frank Garvan: List of Publications |url=http://www.qseries.org/fgarvan/publist.html |accessdate=22 March 2019}} 5. ^ , retrieved 2016-01-26. 6. ^{{cite journal|last=Dyson|first=Freeman J.|title=Some Guesses in The Theory of Partitions|journal=Eureka (Cambridge)|year=1944|volume=8|pages=10–15|url=https://books.google.com/books?id=nnyNUidX1OMC&pg=PA51&lpg=PA51}} External links
7 : 1955 births|Living people|20th-century American mathematicians|21st-century American mathematicians|Australian mathematicians|Number theorists|University of Florida faculty |
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