We use the recently established higher-level Bailey lemma and Bose–Fermi polynomial identities for the minimal models M(p, p) to demonstrate the existence of a Bailey flow from M(p, p) to the coset models (A (1) 1 )N ×(A (1) 1 )N ′/(A (1) 1 )N+N ′ where N is a positive integer and N ′ is fractional, and to obtain Bose–Fermi identities for these models. The fermionic side of these identities is ...

We use the recently established higher-level Bailey lemma and Bose–Fermi polynomial identities for the minimal models M(p, p) to demonstrate the existence of a Bailey flow from M(p, p) to the coset models (A (1) 1 )N ×(A (1) 1 )N ′/(A (1) 1 )N+N ′ where N is a positive integer and N ′ is fractional, and to obtain Bose–Fermi identities for these models. The fermionic side of these identities is ...

Given an arbitrary ordered pair of coprime integers (a, b) we obtain a pair of identities of the Rogers–Ramanujan type. These identities have the same product side as the (first) Andrews–Gordon identity for modulus 2ab ± 1, but an altogether different sum side, based on the representation of (a/b − 1)±1 as a continued fraction. Our proof, which relies on the Burge transform, first establishes a...

We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc − acb − bac + bca + cab − cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree 7 which alternates in 6 arguments, and no new identities in degree 9. We use the representation ...

We obtain some new identities for the generalized Fibonacci polynomial by a approach, namely, Q(x) matrix.
 These including Cassini type identity and Honsberger formula can be applied to polynomial
 sequences such as polynomials, Lucas Pell Pell-Lucas polynomials so on, which
 generalize previous results in references.