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David Bressoud - Research Articles

  • Three alternating sign matrix identities in search of bijective proofs. accepted for publication in Advances in Applied Mathematics. Available as Postscript file or as arXiv:math.CO/0007114 at xxx.lanl.gov
  • Change of base in Bailey pairs, with M. Ismail and D. Stanton. The Ramanujan Journal. 4 (2000), no. 4, 435--453. Available as Tex or PostScript document.
  • A Family of Partition Identities Proved Combinatorially, with Jose Plinio O. Santos and Paulo Mondek. The Ramanujan Journal, Vol: 4, 2000, Pages: 311--315 Available as TeX file.
  • Elementary Proofs of Identities for Schur Functions and Plane Partitions, The Ramanujan Journal, Vol: 4, 2000, Pages: 69--80. Available as TeX file.
  • An elementary proof of the MacMahon conjecture. J. Algebraic Combinatorics. 7:253-257. 1998.Available as TeX file.
  • The Borwein conjecture and partitions with prescribed hook differences. pages 133-150 in The Foata Festschrift, Desarmenien, Kerber, Strehl, eds., Imprimerie Louis-Jean, Gap, 1996. Available as TeX file.
  • The Borwein conjecture and partitions with prescribed
    hook differences. The Electronic Journal of Combinatorics.
    R4, vol. 3 (no. 2). 1996. Available as
    TeX file.
  • with S.Y. Wei. Combinatorial equivalence of definitions of
    the Schur function. Grosswald Memorial Volume. American Math. Soc., Providence, R.I., 1993.
  • with S.Y. Wei. Determinental formulae for complete
    symmetric functions. J. Combinatorial Theory, A. 1992. 60:277--286.
  • Unimodality of Gaussian polynomials, Discrete Math. 99:17--24. 1992.
  • On a cyclotomic unit and related products. J. Number Theory. 38:110--117 (1991).
  • In the land of OZ, pp. 45--55 in q-Series and Partitions, IMA volume 18, D. Stanton, editor, Springer--Verlag, New York, 1989.
  • On the proof of Andrews' q-Dyson conjecture, pp. 31--39 in Number Theory and Related Topics, Oxford University Press, 1989.
  • Lattice paths and the Rogers--Ramanujan identities, pp. 140--172 in Number Theory, Madras 1987, Springer Lecture Notes in Mathematics # 1395. K. Alladi, editor, Springer--Verlag, New York, 1989.
  • with Doron Zeilberger. Generalized Rogers--Ramanujan
    bijections. Adv. Math. 78:42--75 (1989).
  • Almost poised basic hypergeometric series. {\it Proc. Indian Academy of Science}. 97:61--66 (1987).
  • Some directions for multiple hypergeometric series. pp. 99--115 in Ramanujan International Symposium on Analysis, December 26--28, 1987, Pune, India.
  • The Bailey lattice: an introduction, pp. 57--67 in Ramanujan Revisited. G. E. Andrews et al. eds., Academic Press, 1988.
  • Problems on the Z-statistic. Discrete Math. 73:37--48 (1988/89).
  • with A.K. Agarwal. Lattice paths and multiple basic
    hypergeometric series. Pacific J. Math. 135:209--228 (1989).
  • with G.E. Andrews and A.K. Agarwal. The Bailey lattice. J.
    Indian Math. Soc. 51:57--73 (1987).
  • Constant term identities. Proceedings of the Lotharingien Seminar, Burg Feuerstein, Germany, May 1986, IRMA, Strasbourg, France.
  • with Ian Goulden. The generalized plasma in one dimension:
    Evaluation of a partition function. Communications in Mathematical Physics. 110:287--291 (1987).
  • Comments on the proof of the q-Dyson theorem. Proceedings of the Lotharingien Seminar, Bologna, Italy, September 1985, IRMA, Strasbourg, France.
  • Definite integral evaluation by enumeration, partial results on the Macdonald conjectures. pp. 48--57 in Combinatoire Enumerative, Springer Lecture Notes in Mathematics, # 1234, Springer--Verlag, New York, 1986.
  • with G. Andrews, R. J. Baxter, W.J. Burge,. P.J. Forrester,,
    and G. Viennot. Partitions with prescribed hook differences. European J.of Combinatorics. 8:341--350 (1987).
  • with Ian Goulden. Constant term identities extending the
    q-Dyson theorem. Transactions of the American Math. Soc. 291:203--228 (1985).
  • Colored tournaments and Weyl's denominator formula. European J. of Combinatorics. 8:245--255 (1987).
  • Hecke modular forms and q-Hermite polynomials. Illinois J. of Math. 30:185--196 (1986).
  • with Doron Zeilberger. A proof of Andrews' q-Dyson
    conjecture. Discrete Math. 54:201--224 (1985).
  • with George Andrews. On the Burge correspondence between
    partitions and binary words. Rocky Mountain J. 15:225--233 (1985).
  • with Doron Zeilberger. Bijecting Euler's
    partition-recurrence. Amer. Math. Monthly. 92:54--55 (1985).
  • with George Andrews. Identities in combinatorics III.
    Discrete Math. 49:223--236 (1984).
  • with M.V. Subbarao. On Uchimura's connection between
    partitions and number of divisors. Canadian Math. Bull. 27:143--145 (1983).
  • Variation on a partition theorem of Schur. Ars Combinatoria. 15:267--273.
  • A matrix inverse. Proc. Amer. Math. Soc. 88:446--448 (1983).
  • An easy proof of the Rogers--Ramanujan identities. J. Number Theory. 16:235--241 (1983).
  • with Doron Zeilberger. A short Rogers--Ramanujan
    bijection. Discrete Math. 38:313--315 (1982).
  • Theta function identities and orthogonal polynomials. pp 325-332 in Lecture Notes in Math. #899, Springer-Verlag, New York, 1981.
  • The Rogers--Ramanujan identities. (solution to problem 74-12). SIAM Review. 23:101--104 (1981).
  • Some identities for terminating q-series. Math. Proc. Cambridge Phil. Soc. 89:211-223 (1981).
  • Linearization and related formulas for q-ultraspherical polynomials. SIAM J. Math. Anal. 12:161--168 (1981).
  • An analytic generalization of the Rogers--Ramanujan identities with interpretation. Quart. J. Oxford. 31:385--399 (1981).
  • On partitions, orthogonal polynomials and the expansion of certain infinite products. Proc. London Math. Soc. 42:478--500 (1981).
  • On the value of Gaussian sums. J. Number Theory. 13:88--94 (1981).
  • A note on gap-frequency partitions. Pacific J. Math. 89:1--6 (1980).
  • A simple proof of Mehler's formula for $q$-Hermite polynomials. Indiana Math. J. 29:577--580 (1980).
  • A combinatorial proof of Schur's 1926 partition theorem. Proc. Amer. Math. Soc. 79:338--340 (1980).
  • Extension of the partition sieve. J. Number Theory. 12:87--100.Analytic and combinatorial generalizations of the
    Rogers--Ramanujan identities
  • Analytic and combinatorial generalizations of the
    Rogers--Ramanujan identities. Memoir \# 227 of the American Math. Soc., 1980.
  • with George Andrews. Vanishing coefficients in infinite
    product expansions. J. Australian Math. Soc. Series A 27:199--202 (1979).
  • On a partition theorem of G\"{o}llnitz. J. fur die reine und ang. Mat. 305:215--217 (1979).
  • A generalization of the Rogers--Ramanujan identities for all moduli. J. Comb. Theory. 27:64--68 (1979).
  • Applications of Andrews' basic Lauricella transformation. Proc. Amer. Math. Soc. 72:89--94 (1978).
  • A new family of partition identities. Pacific J. Math. 77:71--74 (1978).
  • Some identities involving Rogers--Ramanujan-type functions. J. London Math Soc. 16(2):9--18 (1977).

 



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