Overpartitions

Transactions of the American Mathematical Society

Volumn 356, Issue 4, 2004, Pages 1623-1635

  Corteel, Sylvie ^a   Lovejoy, Jeremy ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1642330015     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-03-03328-2     Document Type: Article

References (23)

1. K. Alladi, A fundamental invariant in the theory of partitions, Topics in Number Theory, Math. Appl. 467, Kluwer, Dordrecht, 1999. MR 2000e:05011
2. G. E. Andrews, On a calculus of partition functions, Pacific J. Math. 31 (1969), 555-562. MR 40:7128
3. G .E. Andrews, Generalizations of the Durfee square, J. London Math. Soc. 3 (1971), 563-570. MR 45:80
4. G. E. Andrews, Problems and prospects for basic hypergeometric functions, Theory and Application of Special Functions, Academic Press, New York, 1975. MR 53:3372
5. G. E. Andrews, Partitions: Yesterday and Today, New Zealand Mathematical Society, Wellington, New Zealand, 1979. MR 81b:01015
6. G. E. Andrews, Partitions and Durfee dissection, Amer. J. Math. 101 (1979), 735-742. MR 80h:10020
7. G. E. Andrews, Ramanujan's "lost" notebook I. Partial 9 functions, Adv. Math. 41 (1981), 137-172. MR 83m:10034a
8. G. E. Andrews, The Theory of Partitions, Cambridge University Press, Cambridge, 1998. MR 99c:11126
9. G. E. Andrews, Generalized Frobenius partitions, Mem. Amer. Math. Soc. 49 (1984), no. 301. MR 85m:11063
10. G. E. Andrews, F. J. Dyson, and D. Hickerson, Partitions and indefinite quadratic forms, Invent. Math. 91 (1988), 391-407. MR 89f:11071
11. G. E. Andrews, J. Jimenez-Urroz, and K. Ono, q-series identities and values of certain L-functions, Duke Math. J. 108 (2001), 395-419. MR 2002e:11055
12. D. Bressoud, and M. Subbarao, On Uchimura's connection between partitions and the number of divisors, Canad. Math. Bull. 27 (1984), no. 2, 143-145. MR 851:11087
13. R. Chapman, Partition identities arising from involutions, Australas. J. Combin. 27 (2003), 285-291.
14. S. Corteel, Particle seas and basic hypergeometric series, Adv. Appl. Math., to appear.
15. S. Corteel and J. Lovejoy, Frobenius partitions and the combinatorics of Ramanujan's 1Ψl summation, J. Combin. Theory Ser. A 97 (2002), 177-183. MR 2002k:11181
16. N. J. Fine, Basic Hypergeometric Series and Applications, American Mathematical Society, Providence, RI, 1988. MR 91j:33011
17. G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990. MR 91d:33034
18. J. T. Joichi and D. Stanton, Bijective proofs of basic hypergeometric series identities, Pacific J. Math. 127 (1987), 103-120. MR 88h:33004
19. J. Lovejoy, A Bailey lattice, Proc. Amer. Math. Soc., to appear.
20. I. Pak, Partition bijections: A survey, preprint.
21. K. Uchimura, An identity for the divisor generating function arising from sorting theory, J. Combin. Theory Ser. A 31 (1981), 131-135. MR 82k:05015
22. S. O. Warnaar, Partial theta functions I. Beyond the lost notebook, preprint.
23. J. Zeng, The q-variations of Sylvester's bijection between odd and strict partitions, preprint.