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E. Andrews and R. J. Baxter, A motivated proof of the Rogers-Ramanujan identities, Amer. Math. Monthly, 96 (1989), 401–409. E. Andrews 5. G. E. Andrews and K. Eriksson, Integer Partitions, Cambridge University Press, Cambridge, 2004. 6. A. Berkovich and F. Garvan, Dissecting the Stanley partition function, J. Comb. Th. (A), 112 (2005), 277–291. 7. H. G¨ollnitz, Partitionen mit Differenzenbedingungen, J. reine u. angew. , 225 (1965), 154–190. 8. B. Gordon, A combinatorial generalization of the Rogers-Ramanujan identities, Amer.

The secret is to adjust the anti-telescoping. n; j /. 1 q 8n 14 / cancels with the same factor in Hn 1 . n; 0/ is clear upon inspection. E. n; 1/ has nonnegative coefficients for n 2. n; j / has nonnegative coefficients. Also because 1 q 6 is in the denominator, we see that the coefficient of q 8j C4 is 1. n; j / is zero. n; j / has only one negative coefficient which is 1 and occurs for q 8j C9 . This requires an analysis analogous to that in Sect. 3. n; j / (excluding 6 and 9). We shall say that 6-partitions (a new definition from that in Sect.

2. x/ > 0g also satisfies it. 2 shows the linear extremal function for the set fxy 2 example, is equal to that of the set fxy 2 > 0g. The former is not contained in a p half-space, while the latter is. jzj/ equal to 0 on the set fxy 2 > 0g, this set does not satisfy the no small functions condition. Hence, it fails the linear bound property. The set fxy 2 0g, even though it is not contained in a half-space. It is contained in a half-space plus a pluripolar set. 3. x/ > 0g, where P is a real homogeneous polynomial.