Iap Lecture January 28, 2000: the Rogers–ramanujan Identities at Y2k
نویسنده
چکیده
The Rogers-Ramanujan identities have reached the ripe-old age of one hundred and five and are still the subject of active research. We will discuss their fascinating history, some of the number theory and combinatorics they encapture, and what they have to do with the 1998 Nobel Prize in physics. 1. The Rogers–Ramanujan identities In this lecture you will be introduced to the Rogers–Ramanujan identities, you will learn some of their history and their fascinating relation to combinatorics and physics. The Rogers–Ramanujan identities are
منابع مشابه
Schur ' s Determinants and Partition
Garrett, Ismail, and Stanton gave a general formula that contains the Rogers{ Ramanujan identities as special cases. The theory of associated orthogonal polynomials is then used to explain determinants that Schur introduced in 1917 and show that the Rogers{Ramanujan identities imply the Garrett, Ismail, and Stanton seemingly more general formula. Using a result of Slater a continued fraction is...
متن کاملPartial-sum Analogues of the Rogers–ramanujan Identities
A new polynomial analogue of the Rogers–Ramanujan identities is proven. Here the product-side of the Rogers–Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials.
متن کاملNew Weighted Rogers-ramanujan Partition Theorems and Their Implications
This paper has a two-fold purpose. First, by considering a reformulation of a deep theorem of Göllnitz, we obtain a new weighted partition identity involving the Rogers-Ramanujan partitions, namely, partitions into parts differing by at least two. Consequences of this include Jacobi’s celebrated triple product identity for theta functions, Sylvester’s famous refinement of Euler’s theorem, as we...
متن کاملPartial-Sum Analogues of the Rogers - Ramanujan Identities
A new type of polynomial analogue of the Rogers–Ramanujan identities is proven. Here the product-side of the Rogers–Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials.
متن کامل