Combinatorics

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By George E. Andrews, Peter Paule, Axel Riese (auth.), Anton Betten, Axel Kohnert, Reinhard Laue, Alfred Wassermann (eds.)

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Additional info for Algebraic Combinatorics and Applications: Proceedings of the Euroconference, Algebraic Combinatorics and Applications (ALCOMA), held in Gößweinstein, Germany, September 12–19, 1999

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Nl , .. 2n x 01 x n1 000A2n; j 1 1 2 ° 28 George E. Andrews, Peter Paule, Axel Riese, and Volker Strehl = n ~ • ( Xo . Xj )q . . ;-1 . ]_1Xj-2) >-;-2 Xj-1XJ - 1- ) Xj-1X2 , "i - 1 We now note that for j 2:: 2 So (31) implies the recurrence (32) It is interesting to note that once the recurrence (32) has been found, here by using 0-calculus, it can be also proved by straight-forward combinatorial reasoning. Combinatorial proof of (32). =l {c 1+1(2m), CJ+t(2m- 1), if n =2m, if n =2m- 1 First, suppose that n = 2m and let be the set of Cayley compositions with j + 1 parts ending in 2m.

Math. 52 (1992), 37- 43. 9. A. E. Brouwer: The linear spaces on 15 points. Ars Combin. 12 (1981), 3-35. 10. P. Dembowski: Finite geometries. Classics in Mathematics. Springer-Verlag, Berlin, 1997. Reprint of the 1968 original. 11. C. Colbourn, J. Dinitz: CRC Handbook of Combinatorial Designs, CRC press, Boca Raton, New York, London, Tokyo, 1996. 12. G. Heathcote: Linear spaces on 16 points. J. Combin. Des. 1 (1993), 359-378. 13. 1; Aachen, St. Andrews, 1999.

Andrews, The Theory of Partitions, Encyclopedia of Mathematics and Its Applications, Vol. -C. , Addison-Wesley, Reading, 1976. ) 2. E. Andrews, The Rogers-Ramanujan reciprocal and Minc's partition function, Pacific J. Math. 95 (1981), 251-256. 3. E. E. ), Prog. Math. 161, Birkhäuser, Boston, 1998, pp. 1-22. 4. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis III: The Omega package, (to appear). 5. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis VI: The fast algorithm, (in preparation).

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