منابع مشابه
Lattice Paths and Rogers Identities
Recently we interpreted five q-series identities of Rogers combinatorially by using partitions with “n + t copies of n” of Agarwal and Andrews [1]. In this paper we use lattice paths of Agarwal and Bressoud [2] to provide new combinatorial interpretations of the same identities. This results in five new 3-way combinatorial identities.
متن کاملOverpartitions, lattice paths, and Rogers-Ramanujan identities
Abstract. We extend partition-theoretic work of Andrews, Bressoud, and Burge to overpartitions, defining the notions of successive ranks, generalized Durfee squares, and generalized lattice paths, and then relating these to overpartitions defined by multiplicity conditions on the parts. This leads to many new partition and overpartition identities, and provides a unification of a number of well...
متن کاملCard Deals, Lattice Paths, Abelian Words and Combinatorial Identities
We give combinatorial interpretations of several related identities associated with the names Barrucand, Strehl and Franel, including one for the Apéry numbers, ∑n k=0 (n k )(n+k k ) ∑k j=0 (k j 3 = ∑n k=0 (n k )2(n+k k 2 . The combinatorial constructs employed are derangement-type card deals as introduced in a previous paper on Barrucand’s identity, labeled lattice paths and, following a comme...
متن کاملNew Finite Rogers-Ramanujan Identities
We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson’s transformation formula by specialization or through Bailey’s method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.
متن کاملFinite Rogers-Ramanujan Type Identities
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 the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a Maple package which is available for free do...
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ژورنال
عنوان ژورنال: Open Journal of Discrete Mathematics
سال: 2011
ISSN: 2161-7635,2161-7643
DOI: 10.4236/ojdm.2011.12011