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Basis Partitions and RogersRamanujan Partitions
"... Every partition has, for some d, a Durfee square of side d. Every partition # with Durfee square of side d gives rise to a "successive rank vector" r = (r 1 , , r d ). Conversely, given a vector r = (r 1 , , r d ), there is a unique partition # 0 of minimal size called the basis pa ..."
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partition with r as its successive rank vector. We give a quick derivation of the generating function for b(n, d), the number of basic partitions of n with Durfee square side d, and show that b(n, d) is a weighted sum over all RogersRamanujan partitions of n into d parts. 1. Introduction Every partition
BASIS PARTITIONS AND THE ROGERSRAMANUJAN IDENTITIES
"... Abstract. In this paper, a common generalization of the RogersRamanujan series and the generating function for basis partitions is studied. This leads naturally to a sequence of polynomials, called BsPpolynomials. In turn, the BsPpolynomials provide simultaneously a proof of the RogersRamanujan ..."
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Abstract. In this paper, a common generalization of the RogersRamanujan series and the generating function for basis partitions is studied. This leads naturally to a sequence of polynomials, called BsPpolynomials. In turn, the BsPpolynomials provide simultaneously a proof of the RogersRamanujan
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"... Basis partitions and Rogers–Ramanujan partitions Every partition has, for some d, a Durfee square of side d. Every partition π with Durfee square of side d gives rise to a “successive rank vector ” r = (r1, · · · , rd). Conversely, given a vector r = (r1, · · · , rd), there is a unique partiti ..."
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Basis partitions and Rogers–Ramanujan partitions Every partition has, for some d, a Durfee square of side d. Every partition π with Durfee square of side d gives rise to a “successive rank vector ” r = (r1, · · · , rd). Conversely, given a vector r = (r1, · · · , rd), there is a unique
BASIS PARTITION POLYNOMIALS, OVERPARTITIONS AND THE ROGERSRAMANUJAN IDENTITIES
"... Abstract. In this paper, a common generalization of the RogersRamanujan series and the generating function for basis partitions is studied. This leads naturally to a sequence of polynomials, called BsPpolynomials. In turn, the BsPpolynomials provide simultaneously a proof of the RogersRamanujan ..."
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Abstract. In this paper, a common generalization of the RogersRamanujan series and the generating function for basis partitions is studied. This leads naturally to a sequence of polynomials, called BsPpolynomials. In turn, the BsPpolynomials provide simultaneously a proof of the RogersRamanujan
The RogersRamanujan recursion and intertwining
 Progress in Mathematics 112, Birkhäuser
, 1993
"... operators ..."
Polynomial identities of the Rogers–Ramanujan type
, 1994
"... Presented are polynomial identities which imply generalizations of Euler and Rogers–Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by establishing a graphical onetoone correspondence between th ..."
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Presented are polynomial identities which imply generalizations of Euler and Rogers–Ramanujan identities. Both sides of the identities can be interpreted as generating functions of certain restricted partitions. We prove the identities by establishing a graphical onetoone correspondence between
Gaussian Integrals And The RogersRamanujan Identities
 in ‘ Symbolic computation
, 2001
"... . It is well known that the Fourier transform of a Gaussian is Gaussian. In this paper it is shown that a qanalogue of this integral gives the RogersRamanujan identities. 1. Introduction. The purpose of this paper is to show that a natural qanalogue of the elementary integral (1.1) I(t) = 1 p ..."
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. It is well known that the Fourier transform of a Gaussian is Gaussian. In this paper it is shown that a qanalogue of this integral gives the RogersRamanujan identities. 1. Introduction. The purpose of this paper is to show that a natural qanalogue of the elementary integral (1.1) I(t) = 1 p
Some crystal RogersRamanujan type identities
 III
, 1999
"... Abstract. By using the KMN2 crystal base character formula for the basic A (1) 2module, and the principally specialized WeylKac character formula, we obtain a RogersRamanujan type combinatorial identity for colored partitions. The difference conditions between parts are given by the energy functi ..."
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Abstract. By using the KMN2 crystal base character formula for the basic A (1) 2module, and the principally specialized WeylKac character formula, we obtain a RogersRamanujan type combinatorial identity for colored partitions. The difference conditions between parts are given by the energy
A probabilistic proof of the Rogers–Ramanujan identities
 Bull. London Math. Soc
"... The asymptotic probability theory of conjugacy classes of the finite general groups leads to a probability measure on the set of all partitions of natural numbers. A simple method of understanding these measures in terms of Markov chains is given, leading to an elementary probabilistic proof of the ..."
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of the RogersRamanujan identities. This is compared with work on the uniform measure. The main case of Bailey’s lemma is interpreted as finding eigenvectors of the transition matrix of a Markov chain. It is shown that the viewpoint of Markov chains extends to quivers.
A Determinant Identity that Implies RogersRamanujan
"... 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 RogersRamanujan type identities. Several examples of new RogersRamanujan type identities are given. 1 ..."
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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 RogersRamanujan type identities. Several examples of new RogersRamanujan type identities are given. 1
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