Garvan, Frank G.

• 3889559
  Frye, Jie(1-BHCC); Garvan, Frank(1-FL)
  Automatic proof of theta-function identities. (English summary) Elliptic integrals, elliptic functions and modular forms in quantum field theory, 195-258,
  Texts Monogr. Symbol. Comput., Springer, Cham, 2019.
  11F27 (11Y16 68T15 68W30)
• 3885143
  Garvan, F. G.(1-FL)
  Transformation properties for Dyson's rank function. (English summary)
  Trans. Amer. Math. Soc. 371 (2019), no. 1, 199-248.
  11F37 (05A19 11B65 11F11 11P82 11P83 11P84 33D15)
  
• 3843270
  Garvan, Frank(1-FL); Schlosser, Michael J.(A-WIENM)
  Combinatorial interpretations of Ramanujan's tau function. (English summary)
  Discrete Math. 341 (2018), no. 10, 2831-2840.
  11F11 (05A30 11P81)
  
• 3791622
  Garvan, F. G.(1-FL)
  Weighted partition identities and divisor sums. (English summary) Frontiers in orthogonal polynomials and $q$$q$-series, 239-249,
  Contemp. Math. Appl. Monogr. Expo. Lect. Notes, 1, World Sci. Publ., Hackensack, NJ, 2018.
  05A17 (05A19 11P82 11P84 33D15)
  
• 3773907
  Analytic number theory, modular forms and $q$$q$-hypergeometric series.
  Proceedings of the Gainsville Number Theory Conference (ALLADI 60) in honor of Krishna Alladi's 60th birthday held at University of Florida, Gainsville, Fl, March 2016. Edited by George E. Andrews and Frank Garvan. Springer Proceedings in Mathematics & Statistics, 221. Springer, Cham, 2017. l+736 pp. ISBN: 978-3-319-68376-8; 978-3-319-68375-1
  11-06 (05-06 33-06)
  
• 3519478
  Garvan, F. G.(1-FL); Jennings-Shaffer, C.(1-ORS)
  Exotic Bailey-Slater SPT-functions II: Hecke-Rogers-type double sums and Bailey pairs from groups A, C, E. (English summary)
  Adv. Math. 299 (2016), 605-639.
  11P82 (11P83 33D15)
  
• 3345301
  Garvan, F. G.(1-FL)
  Congruences and relations for $r$$r$-Fishburn numbers. (English summary)
  J. Combin. Theory Ser. A 134 (2015), 147-165.
  11B75
  
• 3296723
  Garvan, F. G.(1-FL)
  Universal mock theta functions and two-variable Hecke-Rogers identities. (English summary)
  Ramanujan J. 36 (2015), no. 1-2, 267-296.
  11F27 (11F37 11P82 33D15)
  
• 3308071
  Ramanujan 125.
  Proceedings of the International Conference "Ramanujan 125'' held at the University of Florida, Gainesville, FL, November 5-7, 2012. Edited by Krishnaswami Alladi, Frank Garvan and Ae Ja Yee. Contemporary Mathematics, 627. American Mathematical Society, Providence, RI, 2014. x+174 pp. ISBN: 978-1-4704-1078-0
  11-06 (05-06 33-06)
  
• 3277048
  Garvan, Frank G.(1-FL); Jennings-Shaffer, Chris(1-FL)
  The spt-crank for overpartitions.
  Acta Arith. 166 (2014), no. 2, 141-188.
  05A17 (11P82 11P83)
  
• 3239588
  Garvan, Frank G.(1-FL); Sellers, James A.(1-PAS)
  Congruences for generalized Frobenius partitions with an arbitrarily large number of colors. (English summary)
  Integers 14 (2014), Paper No. A7, 5 pp.
  05E05
  
• 3189985
  Garvan, Frank G.(1-FL); Jennings-Shaffer, Chris(1-FL)
  Hecke-type congruences for Andrews' SPT-function modulo 16 and 32. (English summary)
  Int. J. Number Theory 10 (2014), no. 2, 375-390.
  11P82 (05A17 11F33 11F37 11P83)
  
• 3155260
  Computational and analytical mathematics.
  In honor of Jonathan Borwein's 60th birthday. Papers from the workshop (JonFest) held at Simon Fraser University, Burnaby, BC, May 16–20, 2011. Edited by David H. Bailey, Heinz H. Bauschke, Peter Borwein, Frank Garvan, Michel Théra, Jon D. Vanderwerff and Henry Wolkowicz. Springer Proceedings in Mathematics & Statistics, 50. Springer, New York, 2013. xiii+701 pp. ISBN: 978-1-4614-7621-4; 978-1-4614-7620-7
  49-06 (90-06)
  
• 3081040
  Garvan, F. G.(1-FL)
  Congruences for Andrews' spt-function modulo 32760 and extension of Atkin's Hecke-type partition congruences. (English summary) Number theory and related fields, 165–185,
  Springer Proc. Math. Stat., 43, Springer, New York, 2013.
  11P83 (05A17 11F33 11P82)
  
• 3075591
  Partitions, $q$$q$-series, and modular forms.
  Edited by Krishnaswami Alladi and Frank Garvan. Developments in Mathematics, 23. Springer, New York, 2012. xii+224 pp. ISBN: 978-1-4614-0027-1; 978-1-4614-0028-8
  11-06 (05-06 05Axx)
  
• 3048661
  Chan, Song Heng(SGP-NANT-MPM); Dixit, Atul(1-IL); Garvan, Frank G.(1-FL)
  Rank-crank-type PDEs and generalized Lambert series identities. (English summary)
  Ramanujan J. 31 (2013), no. 1-2, 163–189.
  11F11 (11P82 11P83 33D15)
  
• 3048649
  Alladi, Krishnaswami(1-FL); Garvan, Frank(1-FL); Sills, Andrew(1-GSO)
  Preface [International Conference on $q$$q$-Series, Partitions, and Special Functions in honor of Mourad Ismail for his 65th birthday and Dennis Stanton for his 60th birthday].
  Held at Georgia Southern University, Statesboro, GA, March 14–16, 2011.
  Ramanujan J. 31 (2013), no. 1-2, 1–2.
  01A70 (11-06)
  
• 3040662
  Andrews, George E.(1-PAS); Garvan, Frank G.(1-FL); Liang, Jie(1-FL)
  Self-conjugate vector partitions and the parity of the spt-function.
  Acta Arith. 158 (2013), no. 3, 199–218.
  11P83 (05A17 05A19 11P81 11P82)
  
• 2994105
  Andrews, George E.(1-PAS); Garvan, Frank G.(1-FL); Liang, Jie(1-CFL)
  Combinatorial interpretations of congruences for the spt-function. (English summary)
  Ramanujan J. 29 (2012), no. 1-3, 321–338.
  11P83 (05A17 05A19)
  
• 2922612
  Garvan, F. G.(1-FL)
  Congruences for Andrews' spt-function modulo powers of $5$$5$, $7$$7$ and $13$$13$. (English summary)
  Trans. Amer. Math. Soc. 364 (2012), no. 9, 4847–4873.
  11P83 (05A15 05A17 11F33 11F37 11P82)
  
• 2822233
  Garvan, F. G.(1-FL)
  Higher order spt-functions. (English summary)
  Adv. Math. 228 (2011), no. 1, 241–265.
  11P82 (11F33 33D15)
  
• 2856959
  Garvan, F. G.(1-FL)
  Biranks for partitions into 2 colors. (English summary) Ramanujan rediscovered, 87–111,
  Ramanujan Math. Soc. Lect. Notes Ser., 14, Ramanujan Math. Soc., Mysore, 2010.
  11P83 (05Axx 11F03 11F20)
  
• 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)
• 2634873
  Garvan, Francis Gerard
  GENERALIZATIONS OF DYSON'S RANK (COMBINATORIAL, PARTITIONS, CONGRUENCES).
  Thesis (Ph.D.)–The Pennsylvania State University. 1986. 136 pp.
  ProQuest LLC, Thesis
  
• 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)