Abstract
Generalized Frobeniuspartitionsor F-partitions have recently playedan important role in severalcombinatorial investigations of basic hypergeometric series identities. The goal of this paper isto use the framework ofthese investigationsto interpret families of infinite productsas generating functions for F-partitions.We employ q-series identities and bijective combinatorics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G.E. Andrews, The Theory of Partitions, Cambridge University Press, Cambridge, 1998.
G.E. Andrews, Generalized Frobenius partitions, Mem. Amer. Math. Soc. 49 (1984), no. 301.
G.E. Andrews, q-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra, CBMS 66, American Mathematical Society, Providence, 1986.
G.E. Andrews and D.M. Bressoud, Identities in combinatorics, III: Further aspects of ordered set sortingDiscrete Math. 49(1984), 223–236.
D. Corson, D. Favero, K. Liesinger, and S. Zubairy, Characters and q-series in Q(/), preprint.
S. Corteel, Particle seas and basic hypergeometric seriesAdv. Appl. Math. 31 (2003), 199–214.
S. Corteel and J. Lovejoy, Frobenius partitions and the combinatorics of Ramanujan’s iii summationJ. Combin. Theory Ser. A 97(2002), 177–183.
S. Corteel and J. Lovejoy, OverpartitionsTrans. Amer. Math. Socto appear.
N.J. Fine, Basic Hypergeometric Series and Applications, American Mathematical Society, Providence, RI, 1988.
F. Garvan, Partition congruences and generalizations of Dyson’s rank, PhD Thesis, Penn State, 1986.
G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.
J.T. Joichi and D. Stanton, Bijective proofs of basic hypergeometric series identitiesPacific J. Math. 127(1987), 103–120.
L.W. Kolitsch, Some analytic and arithmetic properties of generalized Frobenius partitions, PhD thesis, Penn State, 1985.
J. Lovejoy, Gordon’s theorem for overpartitionsJ. Combin. Th. Ser. A 103(2003), 393–401.
Padmavathamma, Studies in generalized Frobenius partitions, Ph. D. Thesis, Univ. of Mysore, 1985.
J. Propp, Some variants of Ferrers diagrams.J. Combin. Theory Ser. A52 (1989), no. 1, 98–128.
J.P.O. Santos and D.V. Sills, q-Pell sequences and two identities of V.A. LebesgueDisc. Math. 257(2002), 125–143.
J. Sellers, New congruences for generalized Frobenius partitions with two or three colorsDiscrete Math. 131(1994), 367–373.
J.J. Sylvester, A construtive theory of partitions in three acts, an interact and an exodion, in Collected Math. Papers, vol. 4, pp. 1–83, Cambridge Univ. Press, London and New York, 1912; reprinted by Chelsea, New York, 1974.
A.J. Yee, Combinatorial proofs of generating function identities for F-partitions. J. Combin. Theory Ser. A 102(2003), 217–228.
A.J. Yee, Combinatorial proofs of Ramanujan’s 1¢1 summation and the q-Gauss summation, preprint.
D. Zeilberger, A q-Foata proof of the q-Saalschutz identity, European J. Combin. 8 (1987), 461–463.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Basel AG
About this paper
Cite this paper
Corteel, S., Lovejoy, J., Yee, A.J. (2004). Overpartitions and Generating Functions for Generalized Frobenius Partitions. In: Drmota, M., Flajolet, P., Gardy, D., Gittenberger, B. (eds) Mathematics and Computer Science III. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7915-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7915-6_2
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9620-7
Online ISBN: 978-3-0348-7915-6
eBook Packages: Springer Book Archive