A curious identity that implies Faber's conjecture

A Determinant Identity that Implies Rogers-Ramanujan

We give a combinatorial proof of a general determinant identity for associated polynomials. This determinant identity, Theorem 2.2, gives rise to new polynomial generalizations of known Rogers-Ramanujan type identities. Several examples of new Rogers-Ramanujan type identities are given.

A curious binomial identity

In this note we shall prove the following curious identity of sums of powers of the partial sum of binomial coefficients.

Vague Existence Implies Vague Identity

A Combinatorial Proof of Sun's \Curious" Identity

A binomial coeÆcient identity due to Zhi-Wei Sun is the subject of half a dozen recent papers that prove it by various analytic techniques and establish a generalization. Here we give a simple proof that uses weight-reversing involutions on suitable con gurations involving dominos and colorings. With somewhat more work, the method extends to the generalization also. 0 Introduction The identity

The Graham Conjecture Implies the Erdös-turán Conjecture

Erdös and Turán once conjectured that any set A ⊂ N with