Overpartition pairs

Jeremy Lovejoy[1]

  • [1] CNRS, LIAFA, Université Denis Diderot 2, Place Jussieu, Case 7014 75251 Paris Cedex 05 (France)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 3, page 781-794
  • ISSN: 0373-0956

Abstract

top
An overpartition pair is a combinatorial object associated with the q -Gauss identity and the 1 ψ 1 summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of recurrences for well-poised basic hypergeometric series and the theory of Bailey chains.

How to cite

top

Lovejoy, Jeremy. "Overpartition pairs." Annales de l’institut Fourier 56.3 (2006): 781-794. <http://eudml.org/doc/10163>.

@article{Lovejoy2006,
abstract = {An overpartition pair is a combinatorial object associated with the $q$-Gauss identity and the $_1\psi _1$ summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of recurrences for well-poised basic hypergeometric series and the theory of Bailey chains.},
affiliation = {CNRS, LIAFA, Université Denis Diderot 2, Place Jussieu, Case 7014 75251 Paris Cedex 05 (France)},
author = {Lovejoy, Jeremy},
journal = {Annales de l’institut Fourier},
keywords = {Partitions; overpartitions; basic hypergeometric series; Bailey chains; partitions},
language = {eng},
number = {3},
pages = {781-794},
publisher = {Association des Annales de l’institut Fourier},
title = {Overpartition pairs},
url = {http://eudml.org/doc/10163},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Lovejoy, Jeremy
TI - Overpartition pairs
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 3
SP - 781
EP - 794
AB - An overpartition pair is a combinatorial object associated with the $q$-Gauss identity and the $_1\psi _1$ summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of recurrences for well-poised basic hypergeometric series and the theory of Bailey chains.
LA - eng
KW - Partitions; overpartitions; basic hypergeometric series; Bailey chains; partitions
UR - http://eudml.org/doc/10163
ER -

References

top
  1. G. E. Andrews, On q -difference equations for certain well-poised basic hypergeometric series, Quart. J. Math. 19 (1968), 433-447 Zbl0165.08202MR237831
  2. G. E. Andrews, Partitions and Durfee dissection, Amer. J. Math. 101 (1979), 735-742 Zbl0409.10006MR533197
  3. G. E. Andrews, F. J. Dyson, D. Hickerson, Partitions and indefinite quadratic forms, Invent. Math. 91 (1988), 391-407 Zbl0642.10012MR928489
  4. G.E. Andrews, q -series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra, CBMS 66 (1984), American Mathematical Society Zbl0594.33001MR858826
  5. C. Bessenrodt, I. Pak, Partition congruences by involutions, Eur. J. Comb. 25 (2004), 1139-1149 Zbl1068.11067MR2095475
  6. F. Brenti, Determinants of super-Schur functions, lattice paths, and dotted plane partitions, Adv. Math. 98 (1993), 27-64 Zbl0796.05090MR1212626
  7. D. M. Bressoud, A generalization of the Rogers-Ramanujan identities for all moduli, J. Combin. Theory Ser.A 27 (1979), 64-68 Zbl0416.10009MR541344
  8. D. Corson, D. Favero, K. Liesinger, S. Zubairy, Characters and q -series in ℚ ( 2 ) , J. Number Theory 107 (2004), 392-405 Zbl1056.11056MR2072397
  9. S. Corteel, Particle seas and basic hypergeometric series, Adv. Appl. Math. 31 (2003), 199-214 Zbl1050.33010MR1985829
  10. S. Corteel, P. Hitczenko, Multiplicity and number of parts in overpartitions, Ann. Comb. 8 (2004), 287-301 Zbl1052.05011MR2161639
  11. S. Corteel, J. Lovejoy, Frobenius partitions and the combinatorics of Ramanujan’s 1 ψ 1 summation, J. Combin. Theory Ser.A 97 (2002), 177-183 Zbl0998.11050MR1879133
  12. S. Corteel, J. Lovejoy, Overpartitions, Trans. Amer. Math. Soc. 356 (2004), 1623-1635 Zbl1040.11072MR2034322
  13. P. Desrosiers, L. Lapointe, P. Mathieu, Jack polynomials in superspace, Commun. Math. Phys. 242 (2003), 331-360 Zbl1078.81033MR2018276
  14. J-F. Fortin, P. Jacob, P. Mathieu, Generating function for K -restricted jagged partitions Zbl1062.05011
  15. J-F. Fortin, P. Jacob, P. Mathieu, Jagged partitions 
  16. G. Gasper, M. Rahman, Basic Hypergeometric Series, (1990), Cambridge University Press, Cambridge Zbl0695.33001MR1052153
  17. S-J. Kang, J-H. Kwon, Crystal bases of the Fock space representations and string functions, J. Algebra 280 (2004), 313-349 Zbl1137.17304MR2081935
  18. J. Lovejoy, Gordon’s theorem for overparitions, J. Combin. Theory Ser.A 103 (2003), 393-401 Zbl1065.11083
  19. J. Lovejoy, Overpartition theorems of the Rogers-Ramanujan type, J. London Math. Soc. 69 (2004), 562-574 Zbl1087.11062MR2050033
  20. J. Lovejoy, Overpartitions and real quadratic fields, J. Number Theory 106 (2004), 178-186 Zbl1050.11085MR2049600
  21. I. Pak, Partition bijections: A survey Zbl1103.05009
  22. L. J. Slater, A new proof of Rogers’s transformations of infinite series, Proc. London Math. Soc. 53 (1951), 460-475 Zbl0044.06102MR43235
  23. A. J. Yee, Combinatorial proofs of Ramanujan’s 1 ψ 1 summation and the q -Gauss summation, J. Combin. Theory Ser.A 105 (2004), 63-77 Zbl1048.11078MR2030140

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.