## List of PublicationsMost 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. Some papers have a PROOF version for proof-reading purposes.
[ABSTRACT] F.G. Garvan,
New fifth and seventh order mock theta function identities
, (17 pages), submitted.
(Posted October 9, 2018)
[PDF] [ABSTRACT] [SUPPLEMENTS] Jie Frye and Frank Garvan,
Automatic Proof of Theta-Function Identities
,
in "Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory", Springer Wien, provisionally accepted.
(Posted July 20, 2018; Updated August 25, 2018) LOG
[ABSTRACT] [PREFACE] Analytic Number Theory, Modular Forms and $q$-Hypergeometric Series;
In Honor of Krishna Alladi's 60th Birthday,
(Edited by G.E. Andrews and F. Garvan),
Springer Proceedings in Mathematics & Statistics,
Vol. 221, Springer, New York, 2018.
Original book: DOI (Posted April 27, 2018) LOG
[PDF] [ABSTRACT] [SUPPLEMENTS] F. Garvan and M. J. Schlosser,
Combinatorial interpretations of Ramanujan's tau function
,
Discrete Math.
341 (2018), no. 10, 2831--2840.
Original article: DOI (Posted June 26, 2016; Updated July 17, 2018) LOG
[PDF] [ABSTRACT] [SUPPLEMENTS] F.G. Garvan,
Weighted partition identities and divisor sums
,
in "Frontiers in Orthogonal Polynomials and q-Series",
Proceedings of a Conference in honor of Mourad Ismail for his 70th birthday,
Orlando, May 10-12, 2015, World Scientific, pp.239-249.
Original article: DOI [MR 3791622] (Posted May 16, 2016; Updated May 20, 2016 and March 27, 2017) LOG
[ArXiv] [PDF] [PROOF] [ABSTRACT] F.G. Garvan,
Transformation properties for Dyson's rank function
,
Trans. Amer. Math. Soc., to appear.
Original article: DOI (Posted January 23, 2016; Updated June 17, 2016, February 23, 2017 and July 20, 2018) LOG
[ArXiv] [PDF] [ABSTRACT] F.G. Garvan and C. Jennings-Shaffer,
Exotic Bailey-Slater SPT-functions II: Hecke-Rogers-type double sums and Bailey pairs From
groups A, C, E
,
Adv. Math. 299 (2016), 605-639.
Original article: DOI [MR 3519478] [ZBL 1348.11079] (Posted January 28, 2015; Updated August 4, 2016) LOG
[ArXiv] [PDF] [ABSTRACT] F.G. Garvan,
Congruences and relations for r-Fishburn numbers
,
J. Combin. Theory Ser. A 134 (2015), 147-165.
Original article: DOI [MR 3345301] (Abstract posted May 13, 2014; PDF posted May 21, 2014; Revised June 20, 2014; Accepted March 13, 2015, Updated March 31,2015) LOG
[ArXiv] [PDF] [ABSTRACT] [VIDEO] F.G. Garvan,
Universal mock theta functions and two-variable Hecke-Rogers identities
,
(Basil Gordon memorial issue) Ramanujan J.
36 (2015), no. 1-2, 267-296.
Springer Nature View-Only:SharedItOriginal article: DOI [MR 3296723 ] (First posted December 24, 2013; PDF posted February 8, 2014; accepted August 1, 2014; updated August 19, 2014) LOG
[ArXiv] [PDF] [ABSTRACT] F.G. Garvan and C. Jennings-Shaffer,
The spt-crank for overpartitions
,
Acta Arith., 166 (2014), no. 2, 141-188.
Original article: DOI [MR 3277048] (First posted November 14, 2013 to the arXiv; Accepted July 8, 2014) LOG
[ArXiv] [PDF] [ABSTRACT] F.G. Garvan and C. Jennings-Shaffer,
Hecke-type congruences for Andrews' spt-function modulo 16 and 32
,
Int. J. Number Theory, 10 (2014), no. 2, 375-390.
(First posted June 6, 2013 to the arXiv; Revised August 22, 2013; Updated September 14, 2013 and May 21, 2014) [LOG] [ArXiv] [PDF] [ABSTRACT] F.G. Garvan and J.A. Sellers,
Congruences for generalized Frobenius partitions with an arbitrarily
large number of colors
,
INTEGERS, 14 (2014), Article A7.
(First posted May 26, 2013 to the arXiv, Updated April 21, 2014) [LOG] [ABSTRACT] Computational and Analytical Mathematics:
In Honor of Jonathan Borwein's 60th Birthday,
Proceedings of the JonFest Workshop
held at Simon Fraser University, Burnaby, BC, May 16-20, 2011,
(Edited by D.H. Bailey, H.H. Bauschke, P. Borwein, F. Garvan,
M. Thera, J.D. Vanderwerff, and Henry Wolkowicz),
Springer Proceedings in Mathematics & Statistics,
Vol. 50, Springer, New York, 2013.
Original article: DOI [MR 3155260] [LOG] [ArXiv] [PDF] [ABSTRACT] [SUPPLEMENTS] S.H. Chan, A. Dixit and F.G. Garvan,
Rank-Crank type PDEs and generalized Lambert series identities
,
Ramanujan J. 31 (2013), no. 1-2, 163-189.
Original article: DOI (First posted December 30, 2011; Updated February 23, 2012 and May 14, 2014) [LOG]
[PDF]
[ABSTRACT]
[PDF] [ABSTRACT] G.E. Andrews, F.G. Garvan and J.L. Liang,
Combinatorial interpretations of congruences for the spt-function
,
(Ramanujan's 125th anniversary special volume)
Ramanujan J. 29 (2012),
no. 1-3, 321--338.
Original article: DOI [MR 2994105] LOG (First posted October 12, 2011; Updated January 11, 2012, February 23, 2012 and December 12, 2012)
[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
,
Number theory and related fields,
165-185,
Springer Proc. Math. Stat.,
43,
Springer, New York, 2013.
(Proceedings
of an International Number Theory Conference in Memory of Alf van der Poorten,
12-16 March, 2012)
[ArXiv] [DVI] [PDF] [ABSTRACT] F.G. Garvan,
Congruences for Andrews' spt-function modulo powers of 5, 7 and 13
,
Trans. Amer. Math. Soc.,
364 (2012), 4847-4873.
NOTE: Please send me any comments. (First posted November 8, 2010; Updated December 14, 2010) Original article: DOI [MR 2922612] [LOG]
[ArXiv] [PDF] [ABSTRACT] F.G. Garvan,
Higher order spt-functions,
Adv. Math. 228 (2011), 241-265.
Original article: DOI [MR 2822233] (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) [MR 2856959] [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.
Springer Nature View-Only:SharedItOriginal 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.
Original article: DOI [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]
[HTML] F.G. Garvan,
Generalizations of Dyson's Rank
,
Ph.D. Thesis,
Pennsylvania State University, 1986.
[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 ( Author's Home Page |