We study the dilogarithm identities from algebraic, analytic, asymptotic, K-theoretic,
combinatorial and representation-theoretic points of view. We prove that a lot of dilogarithm …

A new object is introduced into the theory of partitions that generalizes plane partitions:
cylindric partitions. We obtain the generating function for cylindric partitions of a given shape …

Half a century ago, The Proceedings of the London Mathematical Society published WN
Bailey's influential paper Identities of the Rogers-Ramanujan type [16]. The main result …

It is shown how many of the partial theta function identities in Ramanujan's lost notebook
can be generalized to infinite families of such identities. Key in our construction is the Bailey …

The trinomial coefficients are defined centrally by $\Sigma _ {j=-m}^\infty {(_j^ m) _2}{x^
j}={(1+ x+{x^{-1}})^ m} $. Euler observed that for $-1\leq m\leq 7$, $3 {(_ {\; 0}^{m+ 1}) _2} …

We construct a family of irreducible representations of the quantum continuous gl∞ whose
characters coincide with the characters of representations in the minimal models of the W n …

Using new $ q $-functions recently introduced by Hatayama et al. and by (two of) the
authors, we obtain an A $ _2 $ version of the classical Bailey lemma. We apply our result …

We discuss conjugation and Dyson's rank for overpartitions from the perspective of the
Frobenius representation. More specifically, we translate the classical definition of Dyson's …

Polynomial generalizations of all 130 of the identities in Slater's list of identities of the
Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of …

We present and prove Rogers–Schur–Ramanujan (Bose/Fermi) type identities for the
Virasoro characters of the minimal model M (p, p′). The proof uses the continued fraction …