Garvan, Frank G.
35
papers
- 2310493
Garvan, Frank G.(1-FL); Yesilyurt, Hamza(1-FL)
Shifted and shiftless partition identities. II. (English summary)
Int. J. Number Theory 3 (2007), no. 1, 43--84.
11P83 (05A17)
- 2177037
Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
On the Andrews-Stanley refinement of Ramanujan's partition congruence modulo 5 and generalizations.
(English. English summary)
Trans. Amer. Math. Soc. 358 (2006), no. 2, 703--726 (electronic).
05A17 (11P81 11P83)
- 2177487
Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
Dissecting the Stanley partition function.
(English. English summary)
J. Combin. Theory Ser. A 112 (2005), no. 2, 277--291.
05A17 (11Pxx)
- 2035811
(2005e:11131)
Atkin, A. O. L.(1-ILCC); Garvan, F. G.(1-FL)
Relations between the ranks and cranks of partitions.
(English. English summary)
Rankin memorial issues.
Ramanujan J. 7 (2003), no. 1-3, 343--366.
11P83 (05A17 05A19 11P81)
- 1956245
(2003m:11173)
Garvan, F. G.(1-FL)
Shifted and shiftless partition identities.
Number theory for the millennium, II (Urbana, IL, 2000),
75--92,
A K Peters, Natick, MA, 2002.
11P83 (05A15 05A19 11P81)
- 1932070
(2003g:11115)
Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
Some observations on Dyson's new symmetries of partitions.
(English. English summary)
J. Combin. Theory Ser. A 100 (2002), no. 1, 61--93.
11P81 (05A17 05A19)
- 1880075
(2002h:11006)
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. xii+283 pp. ISBN 1-4020-0101-0
11-06 (00B25 33-06)
- 1834941
(2002f:11140)
Garvan, F. G.(1-FL)
More cranks and $t$-cores.
(English. English summary)
Bull. Austral. Math. Soc. 63 (2001), no. 3, 379--391.
11P83 (05A17)
- 1823627
(2002a:05019)
Garvan, F. G.(1-FL)
A generalization of the Hirschhorn-Farkas-Kra septagonal numbers identity.
(English. English summary)
Discrete Math. 232 (2001), no. 1-3, 113--118.
05A19
- 1701583
(2000f:33001)
Garvan, Frank(1-FL)
A $q$-product tutorial for a $q$-series MAPLE package.
(English. English summary)
The Andrews Festschrift (Maratea, 1998).
Sém. Lothar. Combin. 42 (1999), Art. B42d, 27 pp. (electronic).
33-04 (05A30 33Dxx 68W30)
- 1691317
(2000c:11169)
Garvan, Frank(1-FL)
Modular functions, Maple and Andrews' 10th problem.
(English. English summary)
Topics in number theory (University Park, PA, 1997),
163--179,
Math. Appl., 467,
Kluwer Acad. Publ., Dordrecht, 1999.
11P82 (11F03)
- 1483915
(98j:11030)
Borwein, J. M.(3-SFR); Garvan, F. G.(1-FL)
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.
11F20 (11Y60)
- 1395412
(97j:11010)
Garvan, Frank G.(1-FL)
Ramanujan's theories of elliptic functions to alternative bases---a symbolic excursion.
(English. English summary)
Symbolic computation in combinatorics $\Delta\sb 1$ (Ithaca, NY, 1993).
J. Symbolic Comput. 20 (1995), no. 5-6, 517--536.
11B65 (33E05)
- 1354548
(97b:11060)
Garvan, Frank G.(1-FL)
A combinatorial proof of the Farkas-Kra theta function identities and their generalizations.
(English. English summary)
J. Math. Anal. Appl. 195 (1995), no. 2, 354--375.
11F27 (05A19 33D10)
- 1311903
(97h:33034)
Berndt, Bruce C.(1-IL); Bhargava, S.(6-MYSO); Garvan, Frank G.(1-FL)
Ramanujan's theories of elliptic functions to alternative bases.
Trans. Amer. Math. Soc. 347 (1995), no. 11, 4163--4244.
33E05 (11F27 33C05 33D10)
- 1291125
(95e:11115)
Garvan, Frank G.(1-FL)
Generalizations of Dyson's rank and non-Rogers-Ramanujan partitions.
(English. English summary)
Manuscripta Math. 84 (1994), no. 3-4, 343--359.
11P83
- 1284065
(95g:39022)
Garvan, Frank(1-FL)
Cubic modular identities of Ramanujan, hypergeometric functions and analogues of the arithmetic-geometric mean iteration.
(English. English summary)
The Rademacher legacy to mathematics (University Park, PA, 1992),
245--264,
Contemp. Math., 166,
Amer. Math. Soc., Providence, RI, 1994.
39B12 (11F11 33C55)
- 1243610
(94j:11019)
Borwein, J. M.(3-DLHS); Borwein, P. B.(3-DLHS); Garvan, F. G.(3-DLHS)
Some cubic modular identities of Ramanujan.
(English. English summary)
Trans. Amer. Math. Soc. 343 (1994), no. 1, 35--47.
11B65 (11F27 33D10)
- 1237931
(95b:33002)
Borwein, J.(3-DLHS); Borwein, P.(3-DLHS); Garvan, F.(3-DLHS)
Hypergeometric analogues of the arithmetic-geometric mean iteration.
(English. English summary)
Constr. Approx. 9 (1993), no. 4, 509--523.
33C05
- 1227653
(94m:33011)
Hirschhorn, Michael(5-NSW-SM); Garvan, Frank(3-DLHS); Borwein, Jon(3-WTRL-B)
Cubic analogues of the Jacobian theta function $\theta(z,q)$.
(English. English summary)
Canad. J. Math. 45 (1993), no. 4, 673--694.
33D10 (11F27)
- 1207544
(94c:11101)
Garvan, Frank G.(1-FL)
Some congruences for partitions that are $p$-cores.
(English. English summary)
Proc. London Math. Soc. (3) 66 (1993), no. 3, 449--478.
11P83 (11B65 11F33)
- 1187229
(94c:68100)
Garvan, Frank G.(1-FL); Gonnet, Gaston H.(CH-ETHZ-I)
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.
(English. English summary)
J. Symbolic Comput. 14 (1992), no. 2-3, 141--177.
68Q40 (33D80 68R05)
- 1078471
(92b:33054)
Garvan, Frank G.(1-FL); Gonnet, Gaston(3-WTRL-C)
Macdonald's constant term conjectures for exceptional root systems.
Bull. Amer. Math. Soc. (N.S.) 24 (1991), no. 2, 343--347.
33D80 (05A30 17B20 17B25)
- 1055707
(91h:11106)
Garvan, Frank(5-MCQR); Kim, Dongsu(1-MN); Stanton, Dennis(1-MN)
Cranks and $t$-cores.
Invent. Math. 101 (1990), no. 1, 1--17.
11P83 (05A17 20C30 33D80)
- 1055413
(91m:11086)
Garvan, Frank G.(5-MCQR)
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.
11P83 (81T30)
- 1046804
(91d:33001)
Garvan, F. G.(5-MCQR)
A proof of the Macdonald-Morris root system conjecture for $F\sb 4$.
SIAM J. Math. Anal. 21 (1990), no. 3, 803--821.
33B15 (17B20 33C80)
- 1023761
(90j:11102)
Garvan, Frank(1-MN-MA); Stanton, Dennis(1-MN)
Sieved partition functions and $q$-binomial coefficients.
Math. Comp. 55 (1990), no. 191, 299--311.
11P68 (05A19 05A30 11B65)
- 1012520
(91b:11109)
Garvan, Frank G.(5-MCQR)
The crank of partitions mod $8,\;9$ and $10$.
Trans. Amer. Math. Soc. 322 (1990), no. 1, 79--94.
11P83 (05A17 11P81)
- 1019845
(90k:33030)
Garvan, Frank G.(1-MN-MA)
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.
33A75 (05A30 17B20 22E60 33A15)
- 987276
(90d:11115)
Andrews, George E.(1-PAS); Garvan, F. G.(1-WI)
Ramanujan's "lost" notebook. VI. The mock theta conjectures.
Adv. in Math. 73 (1989), no. 2, 242--255.
11P68 (01A60 05A19)
- 965267
(89k:33002)
Garvan, F. G.(1-WI)
A beta integral associated with the root system $G\sb 2$.
SIAM J. Math. Anal. 19 (1988), no. 6, 1462--1474.
33A15 (17B20)
- 938958
(89e:11063)
Garvan, F. G.(1-WI)
Combinatorial interpretations of Ramanujan's partition congruences.
Ramanujan revisited (Urbana-Champaign, Ill., 1987),
29--45,
Academic Press, Boston, MA, 1988.
11P76 (05A17)
- 929094
(89b:11079)
Andrews, George E.(1-PAS); Garvan, F. G.(1-WI)
Dyson's crank of a partition.
Bull. Amer. Math. Soc. (N.S.) 18 (1988), no. 2, 167--171.
11P65 (05A17)
- 920146
(89b:11081)
Garvan, F. G.(1-PAS)
New combinatorial interpretations of Ramanujan's partition congruences mod $5,7$ and $11$.
Trans. Amer. Math. Soc. 305 (1988), no. 1, 47--77.
11P76 (05A17 05A19)
- 733905
(85f:11072)
Garvan, F. G.(5-NSW)
A simple proof of Watson's partition congruences for powers of $7$.
J. Austral. Math. Soc. Ser. A 36 (1984), no. 3, 316--334.
11P76 (05A17)
Last update made
Sat Jul 7 14:01:20 EDT 2007