The combinatorics of certain products

The combinatorics of certain products
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by Don Rawlings

Proc. Amer. Math. Soc. 89 (1983), 560-562

DOI: https://doi.org/10.1090/S0002-9939-1983-0715887-2

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A combinatorial interpretation for the coefficients in the expansion of $\Pi (1 + u{x^j}{y^k}){(1 - u{x^j}{y^k})^{ - 1}}$ is given.

References

George E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. MR 0557013
L. Carlitz, The expansion of certain products, Proc. Amer. Math. Soc. 7 (1956), 558–564. MR 85374, DOI 10.1090/S0002-9939-1956-0085374-X
A. M. Garsia and I. Gessel, Permutation statistics and partitions, Adv. in Math. 31 (1979), no. 3, 288–305. MR 532836, DOI 10.1016/0001-8708(79)90046-X

Aspects combinatoires du calcul des

-séries

Don Rawlings, Generalized Worpitzky identities with applications to permutation enumeration, European J. Combin. 2 (1981), no. 1, 67–78. MR 611934, DOI 10.1016/S0195-6698(81)80023-6
D. P. Roselle, Coefficients associated with the expansion of certain products, Proc. Amer. Math. Soc. 45 (1974), 144–150. MR 342406, DOI 10.1090/S0002-9939-1974-0342406-X