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Peter Paule, Cristian-Silviu Radu. Holonomic relations for modular functions and forms: First guess, then prove. International Journal of Number Theory 17(3), pp. 713-759. 2021. World Scientific, 1793-0421. [url] [bib]
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Ralf Hemmecke, Peter Paule, Silviu Radu. Construction of modular function bases for $Gamma_0(121)$ related to $p(11n+6)$. Integral Transforms and Special Functions 32(5-8), pp. 512-527. 2021. Taylor & Francis, 1065-2469. [url] [bib]
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Peter Paule, Cristian-Silviu Radu. An algorithm to prove holonomic differential equations for modular forms. In: Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2019., Bostan A., Raschel K. (ed.), Springer Proceedings in Mathematics & Statistics 373, pp. 367-420. 2021. Springer, Cham, 978-3-030-84303-8. [url] [bib]
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Peter Paule, Silviu Radu. A proof of the Weierstrass gap theorem not using the Riemann-Roch formula. Annals of Combinatorics 23(19-02), pp. 963-1007. May 2019. Springer, 0218-0006. [url] [bib]
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Christoph Koutschan, Peter Paule. Holonomic Tools for Basic Hypergeometric Functions. In: Frontiers of Orthogonal Polynomials and q-Series, Xin Li, Zuhair Nashed (ed.), pp. 393-416. 2018. World Scientific Publishing, ISBN 978-981-3228-87-0. [url] [pdf] [bib]
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Peter Paule, Cristian-Silviu Radu. Rogers-Ramanujan functions, modular functions, and computer algebra. In: Advances in Computer Algebra - In Honour of Sergei Abramov's 70th Birthday, C. Schneider, E. Zima. (ed.), Springer Proceedings in Mathematics & Statistics 226, pp. 229-280. 2018. Springer, Cham, 978-3-319-73231-2. [url] [pdf] [bib]
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Manuel Kauers, Peter Paule, Greg Reid. Workshop on Symbolic Combinatorics and Algorithmic Differential Algebra. ACM Communications in Computer Algebra 50(Issue 1), pp. 27-34. March 2016. 1932-2240. [pdf] [bib]
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Christoph Koutschan, Peter Paule, Sergei K. Suslov. Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II. In: Algebraic and Algorithmic Aspects of Differential and Integral Operators, Moulay Barkatou and Thomas Cluzeau and Georg Regensburger and Markus Rosenkranz (ed.), Lecture Notes in Computer Science 8372, pp. 135-145. 2014. Springer, Berlin Heidelberg, ISBN 978-3-642-54478-1. [pdf] [bib]
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Peter Paule, Sergei K. Suslov. Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I.. In: Computer Algebra in Quantum Field Theory, Texts and Monographs in Symbolic Computation, Springer, 2013, Carsten Schneider, Johannes Blümlein (ed.), pp. 225-241. 2013. Springer, 978-3-7091-1615-9. [bib]
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S. Gerhold, M. Kauers, C. Koutschan, P. Paule, C. Schneider, B. Zimmermann. Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order. In: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, C. Schneider, J. Bluemlein (ed.), Texts and Monographs in Symbolic Computation , pp. 75-96. 2013. Springer, ISBN-13: 978-3709116159. arXiv:1305.4818 [cs.SC]. [url] [pdf] [bib]
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Peter Paule, Cristian-Silviu Radu. The Andrews-Sellers family of partition congruences. Advances in Mathematics 230(3), pp. 819-838. 2012. 0001-8708. [url] [pdf] [bib]
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George E. Andrews and Peter Paule. MacMahon's Dream. In: Partitions, q-Series, and Modular Forms, K. Alladi and F. Garvan (ed.), Developments in Mathematics 23, pp. 1-12. 2012. Springer, 978-1-4614-0028-8. [bib]
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P. Paule, V. Pillwein. Automatic Improvements of Wallis' Inequality. In: SYNASC 2010, 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, T. Ida and others (ed.), pp. 12-16. 2011. IEEE Computer Society, 0. [pdf] [bib]
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Peter Paule, Silviu Radu. Infinite families of strange partition congruences for broken 2-diamonds . The Ramanujan Journal 23, pp. 409-416. 2010. 1382-4090. [url] [pdf] [bib]
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Peter Paule. Henrici's Friendly Monster Identity Revisited. In: "Advances in Combinatorial Mathematics", Proceedings of the Waterloo Workshop in Computer Algebra 2008, Kotsireas, Ilias S.; Zima, Eugene V. (ed.), pp. 155-163. 2010. Springer, 978-3-642-03561-6. [bib]
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F. Chyzak and P. Paule. Chapter Computer Algebra. In: NIST's Digital Library of Mathematical Foundations, F. Olver et al. (ed.), pp. 0-0. 2010. 0. [bib]
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Peter Paule, Bruno Buchberger, Lena Kartashova, Manuel Kauers, Carsten Schneider, Franz Winkler. Algorithms in Symbolic Computation. In: Hagenberg Research, Bruno Buchberger et al. (ed.), Chapter 1, pp. 5-62. 2009. Springer, 978-3-642-02126-8. [url] [pdf] [bib]
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Peter Paule. The Renaissance of Algorithmic Mathematics. In: Hagenberg Research, Peter Paule (ed.), pp. 6-15. 2009. Springer Berlin-Heidelberg, 978-3-642-02126-8. [bib]
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William Y. C. Chen, Peter Paule, Husam L. Saad. Converging to Gosper's Algorithm. Adv. in Appl. Math. 41(3), pp. 351-364. 2008. 0196-8858. [bib]
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F. Chyzak, P. Paule. Computer Algebra. In: The Digital Library of Mathematical Functions (DLMF), D. Lozier (ed.), pp. n/a-n/a. 2007. National Institute of Standards and Technology (NIST), Gaithersburg, U.S.A., electronic. In preparation. [bib]
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Manuel Kauers, Peter Paule. A Computer Proof of Moll's Log-Concavity Conjecture. Proceedings of the AMS 135(12), pp. 3847-3856. December 2007. ISSN 0002-9939. [ps] [bib]
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P. Paule, C. Schneider. Truncating Binomial Series with Symbolic Summation. INTEGERS. Electronic Journal of Combinatorial Number Theory 7(A22), pp. 1-9. 2007. ISSN 1553-1732. [url] [pdf] [bib]
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G. E. Andrews and P. Paule. MacMahon's Partition Analysis XII: Plane Partitions. Journal of the London Mathematical Society 76(3), pp. 647-666. 2007. London Mathematical Society, 0024-6107. [bib]
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A. Becirovic, P. Paule, V. Pillwein, A. Riese, C. Schneider, J. Schoeberl. Hypergeometric Summation Algorithms for High Order Finite Elements. Computing 78(3), pp. 235-249. 2006. ISSN 0010-485X. Preliminary version available. [url] [pdf] [ps] [bib]
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P. Paule, V. Pillwein, C. Schneider, J. Schöberl. Hypergeometric Summation Techniques for High Order Finite Elements. In: PAMM, , Proceedings of GAMM Annual Meeting 2006 - Berlin61, pp. 689-690. 2006. Wiley InterScience, Weinheim, ISBN. [url] [bib]
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G. E. Andrews, P. Paule, C. Schneider. Plane Partitions VI: Stembridge's TSPP Theorem. Advances in Applied Math. Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud 34(4), pp. 709-739. 2005. ISSN 0196-8858. Preliminary version online. [url] [pdf] [ps] [bib]
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G. E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis X: Plane Partitions with Diagonals.. Southeast Asian Journal Mathematics and Mathematical Sciences 3, pp. 3-14. 2004. ISSN 0972-7752. [pdf] [bib]
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P. Paule, C. Schneider. Computer proofs of a new family of harmonic number identities. Adv. in Appl. Math. 31(2), pp. 359-378. 2003. ISSN 0196-8858. Preliminary version online. [url] [ps] [pdf] [bib]
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P. Paule, V. Strehl. Definite Summation and Hypergeometric Identities. In: Computer Algebra Handbook: Foundations, Applications, Systems, J. Grabmeier, E. Kaltofen, V. Weispfenning (ed.), pp. 91-93. 2003. Springer, ISBN: 3-540-65466-6. [bib]
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P. Paule, O. Scherzer, A. Schoisswohl. Wavelets with Scale Dependent Properties. In: Symbolic and Numerical Scientific Computation, F. Winkler and U. Langer (ed.), Lecture Notes in Comput. Sci. 2630, pp. 255-265. 2003. Springer, ISBN: 0-89871-541-5. [ps] [bib]
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P. Paule, H. Prodinger. Fountains, Histograms, and $q$-Identities. Discrete Math. Theor. Comput. Sci. 6, pp. 101-106. 2003. ISSN 1365-8050. [ps] [bib]
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R. Lyons, P. Paule, A. Riese. A Computer Proof of a Series Evaluation in Terms of Harmonic Numbers. Appl. Algebra Engrg. Comm. Comput. 13, pp. 327-333. 2002. ISSN 0938-1279. [pdf] [bib]
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P. Paule. Finite Actions of Groups. In: The Concise Handbook of Algebra, A.V. Mikhalev, G.F. Pilz (ed.), pp. 119-123. 2002. Kluwer, ISBN 0-7923-7072-4. [bib]
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I. Gutman, P. Paule. The Variance of the Vertex Degrees of Randomly Generated Graphs. Publ. Fac. Electr. Engrg. Ser. Mat. 13, pp. 30-35. 2002. ISSN 0354-124X. [bib]
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G.E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis III: The Omega Package. European J. Combin. 22, pp. 887-904. 2001. ISSN 0195-6698. [pdf] [bib]
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G.E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis VI: A New Reduction Algorithm. Ann. Comb. 5, pp. 251-270. 2001. ISSN 0218-0006. [pdf] [bib]
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G.E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis VII: Constrained Compositions. In: q-Series with Applications to Combinatorics, Number Theory, and Physics, B.C. Berndt and K. Ono (ed.), Contemp. Math. 291, pp. 11-27. 2001. Amer. Math. Soc., ISBN 0-8218-2746-4. [pdf] [bib]
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G.E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis VIII: Plane Partition Diamonds. Adv. in Appl. Math. 27, pp. 231-242. 2001. ISSN 0196-8858. [pdf] [bib]
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G.E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis IX: k-Gon Partitions. Bull. Austral. Math. Soc. 64, pp. 321-329. 2001. ISSN 0004-9727. [pdf] [bib]
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G.E. Andrews, P. Paule, A. Riese, V. Strehl. MacMahon's Partition Analysis V: Bijections, Recursions, and Magic Squares. In: Algebraic Combinatorics and Applications, A. Betten and others (ed.), pp. 1-39. 2001. Springer, ISBN 3-5404-1110-0. [pdf] [bib]
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F. Chyzak, P. Paule, O. Scherzer, A. Schoisswohl, B. Zimmermann. The construction of orthonormal wavelets using symbolic methods and a matrix analytical approach for wavelets on the interval. Experiment. Math. 10, pp. 67-86. 2001. ISSN 1058-6458. [pdf] [bib]
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G.E. Andrews, A. Knopfmacher, P. Paule, B. Zimmermann. Engel Expansions of $q$-Series by Computer Algebra. In: Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, F.G. Garvan and M.E.H. Ismail (ed.), Developments in Mathematics 4, pp. 33-57. 2001. Kluwer, ISBN: 1402001010. [pdf] [bib]
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G.E. Andrews, A. Knopfmacher, P. Paule, H. Prodinger. $q$-Engel Series Expansions and Slater's Identities. Quaestiones Math. 24, pp. 403-416. 2001. ISSN 0379-9468. [pdf] [bib]
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A. Berkovich, P. Paule. Variants of the Andrews-Gordon Identities. Ramanujan J. 5, pp. 391-404. 2001. ISSN 1382-4090. [pdf] [bib]
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A. Berkovich, P. Paule. Lattice Paths, $q$-Multinomials and Two Variants of the Andrews-Gordon Identities. Ramanujan J. 5, pp. 409-424. 2001. ISSN 1382-4090. [pdf] [bib]
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G.E. Andrews, A. Knopfmacher, P. Paule. An infinite family of Engel expansions of Rogers-Ramanujan type. Adv. in Appl. Math. 25, pp. 2-11. 2000. ISSN 0196-8858. [pdf] [bib]
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P. Paule. Algorithmic Problem Solving. In: Encyclopedia of Computer Science, A. Ralston, E.D. Reilly, D. Hemmendinger (ed.), pp. 38-40. 2000. Nature Publishing Group, London, ISBN: 1850328005. [bib]
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Peter Paule. A Mathematica Package for Extended Engel Expansions of q-series., pp. 0-0. 2000. editor: K. Alladi, 0. [bib]
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G.E. Andrews, P. Paule. MacMahon's Partition Analysis IV: Hypergeometric Multisums. Sém. Lothar. Combin. B42i, pp. 1-24. 1999. electronic journal. [pdf] [bib]
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F. Chyzak, I. Gutman, P. Paule. Predicting the number of hexagonal systems with 24 and 25 hexagons. Communications in Mathematical and Computer Chemistry 40, pp. 139-151. 1999. ISSN: 0340-6253. [pdf] [bib]
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S.A. Abramov, P. Paule, M. Petkovsek. $q$-Hypergeometric solutions of $q$-difference equations. Discrete Math. 180, pp. 3-22. 1998. ISSN 0012-365X. [pdf] [bib]
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P. Paule, A. Riese. A Mathematica q-Analogue of Zeilberger's Algorithm Based on an Algebraically Motivated Approach to q-Hypergeometric Telescoping. In: Special Functions, q-Series and Related Topics, M.E.H. Ismail and M. Rahman (ed.), Fields Inst. Commun. 14, pp. 179-210. 1997. Amer. Math. Soc., ISBN 0-8218-0524-X. [pdf] [bib]
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I. Nemes, P. Paule. A Canonical Form Guide to Symbolic Summation. In: Advances in the Design of Symbolic Computation Systems, A. Miola, M. Temperini (ed.), Texts Monogr. Symbol. Comput. , pp. 84-110. 1997. Springer, Wien-New York, ISBN 3211828443. [bib]
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P. Paule. A Classical Hypergeometric Proof of an Important Transformation Formula Found by J.-B. Baillon and R.E. Bruck. In: Theory and Applications of Nonlinear Operators of Accretive and Monotype Type, A. G. Kartsatos (ed.), Lecture Notes in Pure and Appl. Math. 178, pp. 241-242. 1996. Marcel Dekker, ISBN 0824797213. [pdf] [bib]
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P. Paule. A Proof of a Conjecture of Knuth. Experiment. Math. 5, pp. 83-89. 1996. ISSN 1058-6458. [pdf] [bib]
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P. Paule. Greatest Factorial Factorization and Symbolic Summation. J. Symbolic Comput. 20, pp. 235-268. 1995. ISSN 0747-7171. [pdf] [bib]
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P. Paule, M. Schorn. A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities. J. Symbolic Comput. 20, pp. 673-698. 1995. ISSN 0747-7171. [pdf] [bib]
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P. Paule, V. Strehl. Symbolic Summation - Some Recent Developments. In: Computer Algebra in Science and Engineering - Algorithms, Systems, and Applications, J. Fleischer et al. (ed.), pp. 138-162. 1995. World Scientific, Singapore, ISBN 981-02-2319-6. [pdf] [bib]
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P. Paule. Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type. Electron. J. Combin. 1, pp. 1-9. 1994. ISSN 1077-8926. [pdf] [bib]
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G. E. Andrews, P. Paule. Some Questions Concerning Computer-Generated Proofs of a Binomial Double-Sum Identity. J. Symbolic Comput. 16, pp. 147-153. 1993. ISSN 0747-7171. [pdf] [bib]
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R. Folk, A. Kartashov, P. Lisonek, P. Paule. Symmetries in Neural Networks: A Linear Group Approach. J. Phys. A 26, pp. 3159-3164. 1993. ISSN 0305-4470. [bib]
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P. Lisonek, P. Paule, V. Strehl. Improvement of the Degree Setting in Gosper's Algorithm. J. Symbolic Comput. 16, pp. 243-258. 1993. ISSN 0747-7171. [pdf] [bib]
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P. Paule. A Note on Bailey's Lemma. J. Combin. Theory Ser. A 44, pp. 164-167. 1987. ISSN 0097-3165. [pdf] [bib]
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P. Paule. A Remark on a Lemma of Ingleton and Piff and the Construction of Bijections. Bayreuth. Math. Schr. 25, pp. 123-127. 1987. ISSN 0172-1062. [pdf] [bib]
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P. Paule. The Concept of Bailey Chains. Sém. Lothar. Combin. B18f, pp. 1-24. 1987. electronic journal. [pdf] [bib]
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P. Paule. Über das Involutionsprinzip von Garsia und Milne. Bayreuth. Math. Schr. 21, pp. 295-319. 1986. ISSN 0172-1062. [pdf] [bib]
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P. Paule. On Identities of the Rogers-Ramanujan Type. J. Math. Anal. Appl. 107, pp. 255-284. 1985. ISSN 0022-247X. [bib]
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P. Paule. Ein neuer Weg zur q-Lagrangeinversion. Bayreuth. Math. Schr. 18, pp. 1-37. 1985. ISSN 0172-1062. [pdf] [bib]
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P. Paule. Über die Inversionsstatistiken von MacMahon und Goulden-Jackson. Sém. Lothar. Combin. B13b, pp. 1-3. 1985. electronic journal. [pdf] [bib]
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