The Rogers-Ramanujan identities have been studied from the viewpoints of combinatorics, number theory, a ne Lie algebras, statistical mechanics, and conformal eld theory. This note connects the Rogers-Ramanujan identities with the nite general linear groups and the HallLittlewood polynomials of symmetric function theory.

ZF, Auberson YP, Kaang BK, Zhuo M: Upregulation of forebrain NMDA NR2B receptors contributes to behavioral sensitization after inflammation. J Neurosci 2005; 25:11107–16 33. Ji G, Horváth C, Neugebauer V: NR2B receptor blockade inhibits pain-related sensitization of amygdala neurons. Mol Pain 2009; 5:21 34. Gabriel AF, Marcus MA, Walenkamp GH, Joosten EA: The CatWalk method: Assessment of mecha...

Culture is considered an evolutionary adaptation that enhances human reproductive fitness. A common explanation is that social learning, the learning mechanism underlying cultural transmission, enhances fitness by avoiding the extra costs of individual learning. This explanation was disproved by a mathematical model of individual and social learning, showing that social learners can invade a po...

We evaluate several integrals involving generating functions of continuous q-Hermite polynomials in two diierent ways. The resulting identities give new proofs and generalizations of the Rogers-Ramanujan identities. Two quintic transformations are given, one of which immediately proves the Rogers-Ramanujan identities without the Jacobi triple product identity. Similar techniques lead to new tra...

A technique by Rogers-Ramachandran and Ramachandran [Vis. Res. 38 (1998) 71-77] was adapted to evaluate magnocellular (M) and parvocellular (P) visual processing efficiency, with identical task structure, in normal and dyslexic children. A battery of phonological, orthographic and cognitive tasks was administered to assess reading ability and component reading skills in both groups. For the vis...

Combination of solutionsby Gerry Leversha, St. Paul's School, London, England, and Kenneth M. Wilke, Topeka, KS, USA. Let n, b and c be the sides of the triangle. Since the perimeter n+ b+ c = 4n, if b < n then c > 2n, contradicting the triangle inequality. Hence we can take n < b < c < 2n. Furthermore we can assume that n, b and c are coprime; for, if (n; b) = d > 1 say, then djc since c = 3n ...