Abstract
Starting from Macdonald's summation formula of Hall-Littlewood polynomials over bounded partitions and its even partition analogue, Stembridge (Trans. Amer. Math. Soc., 319(2), (1990) 469–498) derived sixteen multiple q-identities of Rogers–Ramanujan type. Inspired by our recent results on Schur functions (Adv. Appl. Math., 27, (2001) 493–509) and based on computer experiments we obtain two further such summation formulae of Hall-Littlewood polynomials over bounded partitions and derive six new multiple q-identities of Rogers–Ramanujan type.
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References
G. E. Andrews, The Theory of Partitions,Encyclopedia of mathematics and its applications,Vol. 2, Addison-Wesley, Reading, Massachusetts, 1976.
G.E. Andrews, “Multiple series Rogers–Ramanujan type identities,” Pacific J. Math. 114(2) (1984) 267–283.
G.E. Andrews, q-Series: Their development and application in analysis, combinatorics, physics, and computer algebra, CBMS Regional Conference Series 66, Amer. Math. Soc., Providence,1986.
D. Bressoud, M. Ismail, and D. Stanton, “Change of base in Bailey Pairs,” The Ramanujan J. 4 (2000), 435–453.
G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of mathematicsand its applications, Vol. 35, Cambridge University Press, Cambridge,1990.
P. Hall, “A partition formula connectedwith Abelian groups,” Comment. Math. Helv. 11(1938), 126–129.
F. Jouhet and J. Zeng, “Somenew identities for Schur functions,” Adv. Appl. Math. 27 (2001) 493–509.
I.G. Macdonald,An elementary proof of a q-binomial identity, q-seriesand partitions (Minneapolis, MN, 1988), 73–75, IMA Vol. Math.Appl., 18, Springer, New York, 1989.
I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edn. Clarendon Press, Oxford, 1995.
L.J. Slater, “A new proof of Rogers'stransformations of infinite series,” Proc. London Math.Soc. 53(2) (1951), 460–475.
L. J. Slater, “Further identities ofthe Rogers–Ramanujan Type,” Proc. London Math. Soc. 54(2), (1951–1952), 147–167.
J. R. Stembridge, “Hall-Littlewoodfunctions, plane partitions, and the Rogers—Ramanujan identities,” Trans. Amer. Math. Soc. 319(2) (1990) 469–498.
S. Veigneau, ACE, an Algebraic Environmentfor the Computer Algebra System MAPLE, http://phalanstere.univ-mlv.fr/ ace, 1998.
S. O. Warnaar, 50 years of Bailey's lemma, in Algebraic Combinatorics and Applications (Gößweinstein, 1999), Springer, Berlin, 2001, 333–347.
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2000 Mathematics Subject Classification: Primary–05A19; Secondary–05A17, 05A30
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Jouhet, F., Zeng, J. New Identities for Hall-Littlewood Polynomials and Applications. Ramanujan J 10, 89–112 (2005). https://doi.org/10.1007/s11139-005-3508-3
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DOI: https://doi.org/10.1007/s11139-005-3508-3