Garvan, Frank G.

• 2822233
  Garvan, F. G.(1-FL)
  Higher order spt-functions. (English summary)
  Adv. Math. 228 (2011), no. 1, 241–265.
  11P82 (11F33 33D15)
  
• 2646759
  Garvan, F. G.(1-FL)
  Congruences for Andrews' smallest parts partition function and new congruences for Dyson's rank. (English summary)
  Int. J. Number Theory 6 (2010), no. 2, 281--309.
  05A18 (11F11 11P81 11P83)
  
• 2681308
  Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
  The GBG-rank and $t$$t$-cores I. Counting and 4-cores. (English summary)
  J. Comb. Number Theory 1 (2009), no. 3, 237–252.
  11P81 (05A17 11P83 33D15)
  
• 2471296
  Bringmann, Kathrin(D-KOLN); Garvan, Frank(1-FL); Mahlburg, Karl(1-MIT)
  Partition statistics and quasiharmonic Maass forms.
  Int. Math. Res. Not. IMRN 2009, no. 1, Art. ID rnn124, 63--97.
  11Fxx (11Pxx 33D15)
  
• 2419190
  Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
  K. Saito's conjecture for nonnegative eta products and analogous results for other infinite products. (English summary)
  J. Number Theory 128 (2008), no. 6, 1731--1748.
  11F20 (11B65 11F27 33D15)
  
• 2402176
  Berkovich, Alexander(1-FL); Garvan, Frank G.(1-FL)
  The BG-rank of a partition and its applications. (English summary)
  Adv. in Appl. Math. 40 (2008), no. 3, 377--400.
  11P81 (05A17 05A19 11P83)
  
• 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)