A correspondence between partitions related to generalizations of the Rogers–Ramanujan identities

Burge, William H.

doi:10.1016/0012-365x(81)90017-0

Cited by 30 publications

(53 citation statements)

References 4 publications

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“…The most direct way of seeing this relationship is to notice that these paths are actually in one-to-one correspondence with partitions (ν 1 , · · · , ν m ) (where m is the total length of the path, to be defined below) satisfying the following condition [7,6,17]:…”

Section: The Two Path Descriptions Of the Parafermionic Z K Modelsmentioning

confidence: 99%

Paths for $${\mathcal{Z}}_k$$ Parafermionic Models

Jacob

Mathieu

2007

Lett Math Phys

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Section: The Two Path Descriptions Of the Parafermionic Z K Modelsmentioning

confidence: 99%

Paths for $${\mathcal{Z}}_k$$ Parafermionic Models

Jacob

Mathieu

2007

Lett Math Phys

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“…The Burge correspondence [10] provides a remarkable bijection between a partition with frequency condition and a (Bressoud-type) lattice path. We present the adaptation of this correspondence to the case of a restricted h-partition and aP…”

Section: A3 Paths and H-partitions: The Bruge Correspondencementioning

confidence: 99%

“…10 It corresponds to the configuration with peaks ordered in decreasing values of the charge (although a peak of charge 1 has to precedes the peaks of charge …”

Section: The Generating Function Of P * [K] Pathsmentioning

confidence: 99%

A new path description for the {\cal M} (k+1,2k+3) models and the dual {\cal Z}_k graded parafermions

Jacob

Mathieu

2007

J. Stat. Mech.

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We present a new path description for the states of the non-unitary M(k + 1, 2k + 3) models. This description differs from the one induced by the Forrester-Baxter solution, in terms of configuration sums, of their restricted-solid-on-solid model. The proposed path representation is actually very similar to the one underlying the unitary minimal models M(k + 1, k + 2), with an analogous Fermi-gas interpretation. This interpretation leads to fermionic expressions for the finitized M(k + 1, 2k + 3) characters, whose infinite-length limit represent new fermionic characters for the irreducible modules. The M(k + 1, 2k + 3) models are also shown to be related to the Z k graded parafermions via a (q ↔ q −1 ) duality transformation.

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“…In particular, can (8.5) be generalized? (11) Many identities in sections 6-8 are subject to rather strange restrictions on the parameters (in particular on ε). Special cases show that they are actually wrong outside the range of these restrictions.…”

Section: Future Directions and Open Problemsmentioning

confidence: 99%

“…(7) Linear partitions with restrictions on the hook differences were considered in a number of articles [1], [2], [3], [5], [6], [10], [11]. The most general result, which includes all the others, is contained in [6].…”

Section: µ R ) Be R-tuples Of Integers and D Be An Integer Withmentioning

confidence: 99%

Cylindric Partitions

Gessel

Krattenthaler

1997

Trans. Amer. Math. Soc.

100

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Abstract.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 that satisfy certain row bounds as a sum of determinants of q-binomial coefficients. In some special cases these determinants can be evaluated. Extending an idea of Burge (J. Combin. Theory Ser. A 63 (1993), 210-222), we count cylindric partitions in two different ways to obtain several known and new summation and transformation formulas for basic hypergeometric series for the affine root system Ar. In particular, we provide new and elementary proofs for two Ar basic hypergeometric summation formulas of Milne (Discrete Math. 99 (1992), 199-246).

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A correspondence between partitions related to generalizations of the Rogers–Ramanujan identities

Cited by 30 publications

References 4 publications

Paths for $${\mathcal{Z}}_k$$ Parafermionic Models

Paths for $${\mathcal{Z}}_k$$ Parafermionic Models

A new path description for the {\cal M} (k+1,2k+3) models and the dual {\cal Z}_k graded parafermions

Cylindric Partitions

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