Rogers-Ramanujan-Slater Type Identities (2009)
James Mc Laughlin, Andrew V. Sills, Peter Zimmer
In this survey article, we present an expanded version of Lucy Slater’s famous list of identities of the Rogers-Ramanujan type, including identities of similar type, which were discovered after the...
On Simplifications of Certain q-Multisums (2008)
Some examples of naturally arising multisum q-series which turn out to have representations as fermionic single sums are presented. The resulting identities are proved using transformation formulas...
5. Exploiting Symmetry and Algebraic Relations (2008)
Andrew V. Sills, Doron Zeilberger, Dedicated Freeman, John Dyson, Irving John Good
A Partition Bijection Related to the Rogers-Selberg Identities and Gordon’s Theorem (2008)
We provide a bijective map from the partitions enumerated by the series side of the Rogers-Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon’s combinatorial...
The Rogers-Ramanujan Identities (2008)
Abstract. A generalized Bailey pair, which contains several special cases considered by Bailey (Proc. London Math. Soc. (2), 50 (1949), 421–435), is derived and used to find a number of new...
q-Pell Sequences and Two Identities of V. A. Lebesgue (2008)
Joséplínio O. Santos, Andrew V. Sills
We examine a pair of Rogers-Ramanujan type identities of V. A. Lebesgue, and give polynomial identities for which the original identities are limiting cases. The polynomial identities turn out to be...
Contemporary Mathematics Disturbing the q-Dyson Conjecture (2008)
Abstract. I discuss the computational methods behind the formulation of some conjectures related to variants on Andrews ’ q-Dyson conjecture. 1.
Bijections and congruences for generalizations of partition identities of Euler and Guy (2007)
James A. Sellers, Andrew V. Sills, Gary L. Mullen
In 1958, Richard Guy proved that the number of partitions of n into odd parts greater than one equals the number of partitions of n into distinct parts with no powers of 2 allowed, which is closely...
Disturbing the Dyson Conjecture, in a generally GOOD (2006)
Dyson’s celebrated constant term conjecture (J. Math. Phys., 3 (1962): 140–156) states that the constant term in the expansion of � 1≦i�=j≦n (1 − xi/xj) aj is the multinomial...
c ○ World Scientific Publishing Company IDENTITIES OF THE ROGERS-RAMANUJAN-SLATER TYPE (2005)
Andrew V. Sills, Communicated Bruce, C. Berndt
It is shown that (two-variable generalizations of) more than half of Slater’s list of 130 Rogers-Ramanujan identities (L. J. Slater, Further identities of the Rogers-Ramanujan type, Proc. London...
Andrew V. Sills, Doron Zeilberger, Dedicated Freeman, John Dyson, Irving John Good
We present a case study in experimental yet rigorous mathematics by describing an algorithm, fully implemented in both Mathematica and Maple, that automatically conjectures, and then automatically...
Andrew V. Sills, Doron Zeilberger, Dedicated Freeman, John Dyson, Irving John Good
We present a case study in experimental yet rigorous mathematics by describing an algorithm, fully implemented in both Mathematica and Maple, that automatically conjectures, and then automatically...
A Combinatorial proof of a partition identity of Andrews and Stanley (2004)
In his paper, “On a partition function of Richard Stanley,” George Andrews proves a certain partition identity analytically and asks for a combinatorial proof.This paper provides...
Identities of the Rogers-Ramanujan-Bailey type (2004)
A multiparameter generalization of the Bailey pair is defined in such a way as to include as special cases all Bailey pairs considered by W. N. Bailey in his paper, “Identities of the...
Bijections and Congruences for Generalizations of Partition Identities of Euler and Guy (2004)
James A. Sellers, Andrew V. Sills, Gary L. Mullen
In 1958, Richard Guy proved that the number of partitions of n into odd parts greater than one equals the number of partitions of n into distinct parts with no powers of 2 allowed, which is closely...
A Combinatorial proof of a partition identity of Andrews and Stanley (2004)
In his paper, On a partition function of Richard Stanley, George Andrews proves a certain partition identity analytically and asks for a combinatorial proof.This paper provides the requested...
Finite Rogers-Ramanujan type identities (2003)
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...
Finite Rogers-Ramanujan type identities (2003)
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...
A combinatorial proof of a partition identity of Andrews and (2003)
In his paper, “On a Partition Function of Richard Stanley, ” George Andrews proves a certain partition identity analytically and asks for a combinatorial proof. This paper provides the requested...
On Series Expansions of Capparelli’s Infinite Product (2003)
Using Lie theory, Stefano Capparelli conjectured an interesting Rogers-Ramanujan type partition identity in his 1988 Rutgers Ph.D. thesis. The first proof was given by George Andrews, using...