List of Publications

Most of the papers are available in DVI and PDF formats. Links to ABSTRACTS and reviews in MATHSCINET and ZENTRALBLATT are provided. The papers are listed in reverse chronological order.

Some papers contain SUPPLEMENTS. These supplements contain MAPLE programs for checking a paper and some additional notes.

[ArXiv] [PDF] [ABSTRACT] [SUPPLEMENTS]
S.H. Chan, A. Dixit and F.G. Garvan, Rank-Crank type PDEs and generalized Lambert series identities , Ramanujan J., to appear.
Original article: DOI
(First posted December 30, 2011; Updated January 29, 2012)
[LOG]

[PDF] [ABSTRACT]
G.E. Andrews, F.G. Garvan and J.L. Liang, Self-conjugate vector partitions and the parity of the spt-function, preprint.
(First posted November 14, 2011; Updated January 10, 2012)
[LOG]

[PDF] [ABSTRACT]
G.E. Andrews, F.G. Garvan and J.L. Liang, Combinatorial interpretations of congruences for the spt-function, Ramanujan J., to appear.
(First posted October 12, 2011; Updated January 11, 2012)
[LOG]

[ABSTRACT] [PREFACE]
Partitions, q-Series and Modular Forms, Proceedings of the conference held at the University of Florida, Gainesville, FL, March 2008 (Edited by Krishnaswami Alladi and Frank Garvan), Developments in Mathematics, 23, Springer, New York, 2012.
DOI
(First posted December 20, 2010)
[LOG]

[ArXiv] [DVI] [PDF] [ABSTRACT]
F.G. Garvan, Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences, preprint.
NOTE: Please send me any comments.
(First posted November 8, 2010; Updated November 13, 2010)
[LOG]

[ArXiv] [DVI] [PDF] [ABSTRACT]
F.G. Garvan, Congruences for Andrews' spt-function modulo powers of 5, 7 and 13 , Trans. Amer. Math. Soc., accepted for publication.
NOTE: Please send me any comments.
(First posted November 8, 2010; Updated December 14, 2010)
[LOG]

[ArXiv] [PDF] [ABSTRACT]
F.G. Garvan, Higher order spt-functions, Adv. Math. 228 (2011), 241-265.
(First posted August 6, 2010; Last updated May 25, 2011)
[LOG]
Original article: DOI

[ArXiv] [DVI] [PDF] [ABSTRACT]
F. G. Garvan, Biranks for partitions into 2 colors, in Ramanujan Rediscovered: Proceedings of a Conference on Elliptic Functions, Partitions, and q-Series in memory of K. Venkatachaliengar: Bangalore, 1-5 June, 2009, N. D. Baruah, B. C. Berndt, S. Cooper, T. Huber, and M. J. Schlosser, eds., Ramanujan Mathematical Society, Mysore, 2010, pp. 89-111.
(First posted September 26, 2009; Updated October 26, 2010)
[LOG]

[ArXiv] [DVI] [PDF] [ABSTRACT]
Alexander Berkovich and Frank G. Garvan, The GBG-Rank and t-Cores I. Counting and 4-Cores, Journal of Combinatorics and Number Theory, 1 (2009), no. 3, 49--64.
[MR 2681308]
(Updated October 26, 2010)

[ArXiv]
K. Bringmann, F. G. Garvan, and K. Mahlburg, Partition statistics and quasiweak Maass forms, Int. Math. Res. Not. IMRN (2009), no. 1, 63-97.
Original article: DOI
[MR 2471296] [ZBL 1156.11021]
(Updated September 3, 2009)

[ArXiv] [DVI] [PDF] [ABSTRACT]
F.G. Garvan, Congruences for Andrews' Smallest Parts Partition Function and New Congruences for Dyson's Rank , Int. J. Number Theory, 6 (2010), no. 2, 1--29.
Original article: DOI
[MR 2646759]
(Updated March 6, 2010)

[ArXiv] [DVI] [PDF] [ABSTRACT]
Alexander Berkovich and Frank G. Garvan, K. Saito's Conjecture for Nonnegative Eta Products and Analogous Results for Other Infinite Products , J. Number Theory, 128 (2008), no. 6, 1731--1748.
Original article: DOI
[MR 2419190] [ZBL 1143.05008]

[ArXiv] [DVI] [PDF] [ABSTRACT]
Alexander Berkovich and Frank G. Garvan, The BG-rank of a partition and its applications, Adv. in Appl. Math. 40 (2008), no. 3, 377 - 400.
Original article: DOI
[MR 2402176]

[ArXiv] [DVI] [PDF] [ABSTRACT]
F.G. Garvan and Hamza Yesilyurt, Shifted and shiftless partition identities II, Int. J. Number Theory, 3 (2007), no. 1, 1--42.
Original article: DOI
[MR 2310493] [ZBL 1125.11057]

[ArXiv] [DVI] [PS] [PDF] [ABSTRACT]
Alexander Berkovich and Frank G. Garvan, On the Andrews-Stanley refinement of Ramanujan's partition congruence modulo $5$ and generalizations, Trans. Amer. Math. Soc. 358 (2006), no. 2, 703--726.
Original article: DOI
[MR 2177037] [ZBL 1088.11073]

[ArXiv] [DVI] [PDF] [ABSTRACT]
Alexander Berkovich and Frank G. Garvan, Dissecting the Stanley partition function, J. Combin. Theory Ser. A 112 (2005), no. 2, 277--291.
Original article: DOI
[MR 2177487] [ZBL pre02235886]

[ArXiv] [DVI] [PDF] [ABSTRACT]
A.O.L. Atkin and F.G. Garvan, Relations between the ranks and cranks of partitions, (Rankin memorial issues) Ramanujan J. 7 (2003), no. 1-3, 343--366.
Original article available at www.springlink.com:
http://springerlink.metapress.com/openurl.asp?genre=article&id=doi:10.1023/A:1026219901284
[MR 2035811] [ZBL 1039.11069]
Warning: Published version has some typos. See [LOG]

[ArXiv] [DVI] [PDF] [ABSTRACT]
Alexander Berkovich and Frank G. Garvan, Some observations on Dyson's new symmetries of partitions, J. Combin. Theory Ser. A 100 (2002), no. 1, 61--93.
Original article: DOI
[MR 1932070] [ZBL 1016.05003]

[DVI] [PDF] [ABSTRACT]
F.G. Garvan, Shifted and shiftless partition identities, Number theory for the millennium, II (Urbana, IL, 2000), 75--92, A K Peters, Natick, MA, 2002.
[MR 1956245] [ZBL 1035.11050]

[DVI] [PDF] [ABSTRACT]
F.G. Garvan, More cranks and $t$-cores, Bull. Austral. Math. Soc. 63 (2001), no. 3, 379--391.
Original article: DOI
[MR 1834941] [ZBL 0985.11050]

[DVI] [PDF] [ABSTRACT]
Garvan, F. G.; A generalization of the Hirschhorn-Farkas-Kra septagonal numbers identity, Discrete Math. 232 (2001), no. 1-3, 113--118.
Original article: DOI
[MR 1823627] [ZBL 0979.05009]

[ABSTRACT]
Symbolic computation, number theory, special functions, physics and combinatorics, Proceedings of the conference held at the University of Florida, Gainesville, FL, November 11--13, 1999 (Edited by Frank G. Garvan and Mourad E. H. Ismail), Developments in Mathematics, 4, Kluwer Academic Publishers, Dordrecht, 2001.
[MR 1880075] [ZBL 0980.00026]

[ABSTRACT]
Frank Garvan, The Maple book, Chapman & Hall/CRC., Boca Raton, 2001.
[ZBL 1005.68185]

[DVI] [PDF] [MWS] [MAPLE PACKAGE] [HTML] [ABSTRACT]
Garvan, Frank; A $q$-product tutorial for a $q$-series MAPLE package, The Andrews Festschrift (Maratea, 1998), Sém. Lothar. Combin. 42 (1999), Art. B42d, 27 pp. ( electronic).
[MR 1701583] [ZBL 1010.11072]

[DVI] [PDF] [ABSTRACT]
Garvan, Frank; Modular functions, Maple and Andrews' 10th problem, Topics in number theory (University Park, PA, 1997), 163--179, Math. Appl., 467, Kluwer Acad. Publ., Dordrecht, 1999.
[MR 1691317] [ZBL 0932.11067]

[ABSTRACT]
Garvan, Frank; Maple V Primer (Release 4), CRC Press, Boca Raton, 1996.
[ZBL 0855.68045]

[DVI] [PDF] [HTML] [ABSTRACT]
J.M. Borwein and F.G. Garvan; Approximations to $\pi$ via the Dedekind eta function. Organic mathematics (Burnaby, BC, 1995), 89--115, CMS Conf. Proc., 20, Amer. Math. Soc., Providence, RI, 1997.
[MR 1483915] [ZBL 893.11050]

[JSTOR] [DVI] [PS] [PDF] [ABSTRACT]
Berndt, Bruce C., Bhargava, S., and Garvan, Frank G.; Ramanujan's theories of elliptic functions to alternative bases, Trans. Amer. Math. Soc. 347 (1995), no. 11, 4163--4244.
Original article: DOI
[MR 1311903] [ZBL 0843.33012]

[DVI] [PDF] [ABSTRACT]
Garvan, Frank G.; A combinatorial proof of the Farkas-Kra theta function identities and their generalizations, J. Math. Anal. Appl. 195 (1995), no. 2, 354--375.
[MR 1354548] [ZBL 0849.11038]

[DVI] [PDF] [ABSTRACT]
Garvan, Frank G.; Ramanujan's theories of elliptic functions to alternative bases---a symbolic excursion, Symbolic computation in combinatorics $\Delta\sb 1$ (Ithaca, NY, 1993), J. Symbolic Comput. 20 (1995), no. 5-6, 517--536.
[MR 1395412] [ZBL 0849.68063]

[JSTOR] [DVI] [PDF] [ABSTRACT]
Borwein, J. M., Borwein, P. B., and Garvan, F. G.; Some cubic modular identities of Ramanujan, Trans. Amer. Math. Soc. 343 (1994), no. 1, 35--47.
[MR 1243610] [ZBL 0799.33012]

[DVI] [PDF] [ABSTRACT]
Garvan, Frank; Cubic modular identities of Ramanujan, hypergeometric functions and analogues of the arithmetic-geometric mean iteration, The Rademacher legacy to mathematics (University Park, PA, 1992), 245--264, Contemp. Math., 166, Amer. Math. Soc., Providence, RI, 1994.
[MR 1284065] [ZBL 0808.33003]

[DVI] [PS] [PDF] [ABSTRACT]
Garvan, Frank G.; Generalizations of Dyson's rank and non-Rogers-Ramanujan partitions, Manuscripta Math. 84 (1994), no. 3-4, 343--359.
[MR 1291125] [ZBL 0819.11043]

[DVI] [PDF] [ABSTRACT]
Hirschhorn, Michael; Garvan, Frank; and Borwein, Jon; Cubic analogues of the Jacobian theta function $\theta(z,q)$, Canad. J. Math. 45 (1993), no. 4, 673--694.
Original article: http://cms.math.ca/cjm/v45/p673
[MR 1227653] [ZBL 0797.33012]

[DVI] [PDF] [ABSTRACT]
Garvan, Frank G.; Some congruences for partitions that are $p$-cores, Proc. London Math. Soc. (3) 66 (1993), no. 3, 449--478.
Original article: DOI
[MR 1207544] [ZBL 0788.11044]

[PDF] [ABSTRACT]
J. Borwein, P. Borwein and F. Garvan, Hypergeometric analogues of the arithmetic-geometric mean iteration,
Constr. Approx. 9 (1993), no. 4, 509--523.
[MR 1237931] [ZBL 0785.33001]

[DVI] [PDF] [ABSTRACT]
Frank G. Garvan and Gaston H. Gonnet, A proof of the two parameter $q$-cases of the Macdonald-Morris constant term root system conjecture for $S(F\sb 4)$ and $S(F\sb 4)\sp \vee$ via Zeilberger's method, J. Symbolic Comput. 14 (1992), no. 2-3, 141--177.
[MR 1187229] [ZBL 0766.33017]

[PS] [PDF] [ABSTRACT]
Frank G. Garvan and Gaston Gonnet, Macdonald's constant term conjectures for exceptional root systems, Bull. Amer. Math. Soc. (N.S.) 24 (1991), no. 2, 343--347.
[MR 1078471] [ZBL 0737.33011]

[DVI] [PDF] [ABSTRACT]
Frank G. Garvan, A number-theoretic crank associated with open bosonic strings, Number theory and cryptography (Sydney, 1989), 221--226, London Math. Soc. Lecture Note Ser., 154, Cambridge Univ. Press, Cambridge, 1990.
[MR 1055413] [ZBL 0717.11043]

[DVI] [PDF] [ABSTRACT]
Frank Garvan, Dongsu Kim, and Dennis Stanton, Cranks and $t$-cores, Invent. Math. 101 (1990), no. 1, 1--17.
[MR 1055707] [ZBL 0721.11039]

[DVI] [PDF] [ABSTRACT]
F.G. Garvan, A proof of the Macdonald-Morris root system conjecture for $F\sb 4$, SIAM J. Math. Anal. 21 (1990), no. 3, 803--821.
[MR 1046804] [ZBL 0711.33001]

[JSTOR] [DVI] [PDF] [ABSTRACT]
Frank G. Garvan, The crank of partitions mod $8$, $9$ and $10$, Trans. Amer. Math. Soc. 322 (1990), no. 1, 79--94.
[MR 1012520] [ZBL 0717.11042]

[DVI] [PDF] [ABSTRACT]
Frank G. Garvan, Some Macdonald-Mehta integrals by brute force, $q$-series and partitions (Minneapolis, MN, 1988), 77--98, IMA Vol. Math. Appl., 18, Springer, New York, 1989.
[MR 1019845] [ZBL 0697.33008]

[JSTOR] [DVI] [PDF] [ABSTRACT]
Frank Garvan, and Dennis Stanton, Sieved partition functions and $q$-binomial coefficients, Math. Comp. 55 (1990), no. 191, 299--311.
[MR 1023761] [ZBL 0702.05008]

[ABSTRACT]
George E. Andrews and F.G. Garvan, Ramanujan's "lost" notebook. VI. The mock theta conjectures, Adv. in Math. 73 (1989), no. 2, 242--255.
[MR 987276] [ZBL 0677.10010]

[DVI] [PDF] [ABSTRACT]
F.G. Garvan, A beta integral associated with the root system $G\sb 2$, SIAM J. Math. Anal. 19 (1988), no. 6, 1462--1474.
[MR 965267] [ZBL 0657.33001]

[HTML] [ABSTRACT]
George E. Andrews and F.G. Garvan, Dyson's crank of a partition, Bull. Amer. Math. Soc. (N.S.) 18 (1988), no. 2, 167--171.
Original article: [PDF]
[MR 929094] [ZBL 0646.10008]

[DVI] [PDF] [ABSTRACT]
F.G. Garvan, Combinatorial interpretations of Ramanujan's partition congruences, Ramanujan revisited (Urbana-Champaign, Ill., 1987), 29--45, Academic Press, Boston, MA, 1988.
[MR 938958] [ZBL 0652.10010]

[JSTOR] [ABSTRACT]
F.G. Garvan, New combinatorial interpretations of Ramanujan's partition congruences mod $5,7$ and $11$, Trans. Amer. Math. Soc. 305 (1988), no. 1, 47--77.
[MR 920146] [ZBL 0641.10009]

[PDF] [ABSTRACT]
F.G. Garvan, A simple proof of Watson's partition congruences for powers of $7$, J. Austral. Math. Soc. Ser. A 36 (1984), no. 3, 316--334.
Original article: DOI
[MR 733905] [ZBL 0533.10006]

[HTML]
F.G. Garvan, Some Congruence Properties of the Partition Function , M. Sc. Thesis, University of New South Wales, 1982.

Created by F.G. Garvan (fgarvan@math.ufl.edu) on June 17, 1995.
Last update made Sun Jan 29 02:03:47 EST 2012.

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