{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T09:13:12Z","timestamp":1773393192681,"version":"3.50.1"},"reference-count":60,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[1999,6,1]],"date-time":"1999-06-01T00:00:00Z","timestamp":928195200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":5160,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Mathematics"],"published-print":{"date-parts":[[1999,6]]},"DOI":"10.1016\/s0012-365x(98)00374-4","type":"journal-article","created":{"date-parts":[[2003,4,23]],"date-time":"2003-04-23T20:16:34Z","timestamp":1051128994000},"page":"249-279","source":"Crossref","is-referenced-by-count":18,"title":["A new multidimensional matrix inverse with applications to multiple q-series"],"prefix":"10.1016","volume":"204","author":[{"given":"Christian","family":"Krattenthaler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Schlosser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0012-365X(98)00374-4_BIB1","first-page":"1","article-title":"Connection coefficient problems and partitions","volume":"vol. 34","author":"Andrews","year":"1979"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB2","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1112\/jlms\/s1-22.3.237","article-title":"A transformation of nearly-poised basic hypergeometric series","volume":"22","author":"Bailey","year":"1947","journal-title":"J. London Math. Soc."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB3","first-page":"421","article-title":"Some identities in combinatory analysis","volume":"49","author":"Bailey","year":"1947"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB4","first-page":"1","article-title":"Identities of the Roger-Ramanujan type","volume":"50","author":"Bailey","year":"1949"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB5","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1006\/aima.1997.1659","article-title":"Generalized bibasic hypergeometric series and their U(n) extensions","volume":"131","author":"Bhatnagar","year":"1977","journal-title":"Adv. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB6","first-page":"211","article-title":"Some identities for terminating q-series","volume":"89","author":"Bressoud","year":"1981"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB7","first-page":"446","article-title":"A matrix inverse","volume":"88","author":"Bressoud","year":"1983"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB8","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1215\/S0012-7094-73-04083-0","article-title":"Some inverse relations","volume":"40","author":"Carlitz","year":"1973","journal-title":"Duke Math. J."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB9","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/0126040","article-title":"An application of MacMahon's Master Theorem","volume":"26","author":"Carlitz","year":"1974","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB10","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1137\/0508023","article-title":"Some expansions and convolution formulas related to MacMahon's Master Theorem","volume":"8","author":"Carlitz","year":"1977","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB11","first-page":"331","article-title":"Multiple binomial and power sums","volume":"6","author":"Carlitz","year":"1980","journal-title":"Houston J. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0195-6698(13)80002-9","article-title":"Some multifold reciprocal transformations with applications to series expansions","volume":"12","author":"Chu","year":"1991","journal-title":"Europ. J. Combin."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB13","first-page":"43","article-title":"Inversion techniques and combinatorial identities \u2014 Jackson's q-analogue of the Dougall-Dixon theorem and the dual formulae","volume":"95","author":"Chu","year":"1995","journal-title":"Compositio Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB14","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF01319097","article-title":"Operatormethoden f\u00fcr q-Identit\u00e4ten","volume":"88","author":"Cigler","year":"1979","journal-title":"Monatsh. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB15","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1002\/sapm1991853243","article-title":"A generalization of the Pfaff-Saalsch\u00fctz theorem","volume":"85","author":"Constantineau","year":"1991","journal-title":"Stud. Appl. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB16_1","series-title":"Integral representation and the computation of combinatorial sums","author":"Egorychev","year":"1977"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB16_2","volume":"vol. 59","author":"Egorychev","year":"1984"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB17_1","article-title":"De serie Lambertiana plurimisque eius insignibus proprietatibus","author":"Euler","year":"1779","journal-title":"Acta Acad. Sci. Petro"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB17_2","first-page":"29","article-title":"De serie Lambertiana plurimisque eius insignibus proprietatibus","volume":"II","author":"Euler","year":"1783"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB18","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1137\/0512020","article-title":"Summation formulas for basic hypergeometric series","volume":"12","author":"Gasper","year":"1981","journal-title":"SIAM J. Math. Anal."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB19","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1090\/S0002-9947-1989-0953537-0","article-title":"Summation, transformation and expansion formulas for bibasic series","volume":"312","author":"Gasper","year":"1989","journal-title":"Trans. Amer. Soc."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4153\/CJM-1990-001-5","article-title":"An indefinite bibasic summation formula and some quadratic, cubic and quartic summation and transformation formulae","volume":"42","author":"Gasper","year":"1990","journal-title":"Canad. J. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB21","article-title":"Basic hypergeometric series","volume":"vol. 35","author":"Gasper","year":"1990"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB22","first-page":"173","article-title":"Application of q-Lagrange inversion to basic hypergeometric series","volume":"277","author":"Gessel","year":"1983","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB23","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1216\/RMJ-1986-16-2-373","article-title":"Another family of q-Lagrange inversion formulas","volume":"16","author":"Gessel","year":"1986","journal-title":"Rocky Moutain J. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB24","unstructured":"I.M. Gessel, D. Sturtevant, A combinatorial proof of Saalsch\u00fctz's theorem, unpublished."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB25","doi-asserted-by":"crossref","first-page":"84","DOI":"10.2307\/2306429","article-title":"Some generalizations of Vandermonde's convolution","volume":"63","author":"Gould","year":"1956","journal-title":"Amer. Math. Monthly"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB26","doi-asserted-by":"crossref","first-page":"409","DOI":"10.2307\/2310165","article-title":"Final analysis of Vandermonde's convolution","volume":"64","author":"Gould","year":"1957","journal-title":"Amer. Math. Monthly"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB27","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1215\/S0012-7094-61-02817-4","article-title":"A series transformation for finding convolution identities","volume":"28","author":"Gould","year":"1961","journal-title":"Duke Math. J."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB28","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1215\/S0012-7094-62-02938-1","article-title":"A new convolution formula and some new orthogonal relations for inversion of series","volume":"29","author":"Gould","year":"1962","journal-title":"Duke Math. J."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB29","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1215\/S0012-7094-64-03131-X","article-title":"A new series transform with application to Bessel, Legrende, and Tchebychev polynomials","volume":"31","author":"Gould","year":"1964","journal-title":"Duke Math. J."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB30","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1215\/S0012-7094-65-03275-8","article-title":"Inverse series relations and other expansions involving Humbert polynomials","volume":"32","author":"Gould","year":"1965","journal-title":"Duke Math. J."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB31","series-title":"Combinatorial Identities","author":"Gould","year":"1972"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB32","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1215\/S0012-7094-73-04082-9","article-title":"Some new inverse series relations","volume":"40","author":"Gould","year":"1973","journal-title":"Duke Math. J."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB33","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/0377-0427(95)00260-X","article-title":"Heine transformations for a new kind of basic hypergeometric series in U(n)","volume":"68","author":"Gustafson","year":"1996","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB34","first-page":"83","article-title":"Determinant evaluations and U(n) extensions of Heine's 2\u03c61-transformations","volume":"vol. 14","author":"Gustafson","year":"1997"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB35","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1007\/BF01443681","article-title":"Ueber die Convergenz der hypergeometrischen Reihen zweier und dreier Ver\u00e4nderlichen","volume":"34","author":"Horn","year":"1889","journal-title":"Math. Ann."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB36","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1007\/BF03014074","article-title":"A q-generalization of Abel's series","volume":"29","author":"Jackson","year":"1910","journal-title":"Rend. Circ. Math. Palermo"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB37","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0012-365X(95)00108-9","article-title":"q-Extensions of identities of Abel-Rothe type","volume":"159","author":"Johnson","year":"1996","journal-title":"Discrete Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB38","article-title":"Multiple Gaussian Hypergeometric Series","author":"Karlsson","year":"1985"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB39","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1090\/S0002-9947-1988-0924765-4","article-title":"Operator methods and Lagrange inversion, a unified approach to Lagrange formulas","volume":"305","author":"Krattenthaler","year":"1988","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB40","doi-asserted-by":"crossref","first-page":"743","DOI":"10.4153\/CJM-1989-034-1","article-title":"Q-analogue of a two variable inverse pair of series with applications to basic double hypergeometric series","volume":"41","author":"Krattenthaler","year":"1989","journal-title":"Canad. J. Math."},{"issue":"552","key":"10.1016\/S0012-365X(98)00374-4_BIB41","article-title":"The major counting of nonintersecting lattice paths and generating functions for tableaux","volume":"155","author":"Krattenthaler","year":"1995","journal-title":"Mem. Amer. Math. Soc."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB42","first-page":"47","article-title":"A new matrix inverse","volume":"124","author":"Krattenthaler","year":"1996"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB43","unstructured":"C. Krattenthaler, M. Schlosser, A q-analogue of MacMahon's Master Theorem and applications, in preparation."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB44","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1007\/BF01204652","article-title":"The Cl Bailey transform and Bailey lemma","volume":"9","author":"Lilly","year":"1993","journal-title":"Constr. Approx."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB45","series-title":"Combinatory Analysis","author":"MacMahon","year":"1915"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB46","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/0022-247X(87)90355-6","article-title":"Basic hypergeometric series very well-poised in U(n)","volume":"122","author":"Milne","year":"1987","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB47","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/aima.1994.1065","article-title":"q-analog of a Whipple's transformation for hypergeometric series in U(n)","volume":"108","author":"Milne","year":"1994","journal-title":"Adv. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB48","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1006\/aima.1997.1658","article-title":"Balanced 3\u03c62 summation theorems for U(n) basic hypergeometric series","volume":"131","author":"Milne","year":"1997","journal-title":"Adv. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB49","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/0012-365X(94)00139-A","article-title":"Consequences of the At and Ct Bailey transform and Bailey lemma","volume":"139","author":"Milne","year":"1995","journal-title":"Discrete Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB50","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/0377-0427(95)00248-0","article-title":"U(n) very-well-poised 10\u03c69 transformations","volume":"68","author":"Milne","year":"1996","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB51","first-page":"161","article-title":"Some cubic summation formulas for basic hypergeometric series","volume":"36","author":"Rahman","year":"1989","journal-title":"Utilitas Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB52","doi-asserted-by":"crossref","first-page":"394","DOI":"10.4153\/CJM-1993-020-8","article-title":"Some quadratic and cubic summation formulas for basic hypergeometric series","volume":"45","author":"Rahman","year":"1993","journal-title":"Can. J. Math."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB53","series-title":"Combinatorial Identities","author":"Riordan","year":"1968"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB54","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1023\/A:1009705129155","article-title":"Multidimensional matrix inversions and Ar and Dr basic hypergeometric series","volume":"1","author":"Schlosser","year":"1997","journal-title":"Ramanujan J."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB55","unstructured":"M. Schlosser, Summation theorems for multidimensional basic hypergeometric series by determinant evaluations, submitted."},{"key":"10.1016\/S0012-365X(98)00374-4_BIB56","first-page":"352","article-title":"Une interpr\u00e9tation de certain solutions de l'\u00e9quation fonctionnelle: F(x + y) = F(x)F(y)","volume":"236","author":"Sch\u00fctzenberger","year":"1953","journal-title":"C. R. Acad. Sci. Paris"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB57","series-title":"Zykel-Enumeration bei lokal-strukturierten Funktionen, Habilitationsschrift","author":"Strehl","year":"1990"},{"key":"10.1016\/S0012-365X(98)00374-4_BIB58","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/0012-365X(92)90379-T","article-title":"Identities of Rothe-Abel-Schl\u00e4fli-Hurwitz-type","volume":"99","author":"Strehl","year":"1992","journal-title":"Discrete Math."}],"container-title":["Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X98003744?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X98003744?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2021,5,5]],"date-time":"2021-05-05T14:50:35Z","timestamp":1620226235000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0012365X98003744"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,6]]},"references-count":60,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1999,6]]}},"alternative-id":["S0012365X98003744"],"URL":"https:\/\/doi.org\/10.1016\/s0012-365x(98)00374-4","relation":{},"ISSN":["0012-365X"],"issn-type":[{"value":"0012-365X","type":"print"}],"subject":[],"published":{"date-parts":[[1999,6]]}}}