Related papers: An Iterated Map for the Lebesgue Identity
Alladi studied partition theoretic implications of a two variable generalization of the Lebesgue identity. In this short note, we focus on a slight variation of the basic hypergeometric sum that Alladi studied. We present two new partition…
In this note, we will give a short proof of an identity for cubic partitions.
We prove an identity about partitions with a very elementary formulation. We had previously conjectured this identity, encountered in the study of shifted Jack polynomials (math.CO/9901040). The proof given is using a trivariate generating…
Alternative approaches to Lebesgue integration are considered.
Using the slow triangle map (a type of multi-dimensional continued fraction algorithm), we exhibit a method for generating any number of new identities for subsets of integer partitions.
Ferrers graphs and tables of partitions are treated as vectors. Matrix operations are used for simple proofs of identities concerning partitions. Interpreting partitions as vectors gives a possibility to generalize partitions on negative…
Using a specific form of the triple product identity, polygonal number identities are stated. Further number identities are examined that can be considered identities related to modular sets of numbers. The identities can be used to give…
Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.
A discrete map based on the sum of an integer's distinct primes factors and the sum of its other factors is defined and its iteration is studied.
We obtain a finite form of Jacobi's identity and present a combinatorial proof based on the structure of synchronized partitions.
We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and…
We prove and conjecture some new symmetric function identities, which equate the generating series of 1. Plane partitions, subject to certain restrictions and weightings, and 2. Alternating sign matrices, subject to certain symmetry…
We prove a partition identity conjectured by Lassalle (Adv. in Appl. Math. 21 (1998), 457-472).
We prove two identities of Hall-Littlewood polynomials, which appeared recently in a paper by two of the authors. We also conjecture, and in some cases prove, new identities which relate infinite sums of symmetric polynomials and partition…
A unicellular map, or one-face map, is a graph embedded in an orientable surface such that its complement is a topological disk. In this paper, we give a new viewpoint to the structure of these objects, by describing a decomposition of any…
We present identities for permutations with fixed points. The formulas are based on successive derivations or integrations of the determinant of a particular matrix.
This paper highlights three known identities, each of which involves sums over alternating sign matrices. While proofs of all three are known, the only known derivations are as corollaries of difficult results. The simplicity and natural…
The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…
We prove an identity about partitions, previously conjectured in the study of shifted Jack polynomials (math.CO/9903020). The proof given is using $\lambda$-ring techniques. It would be interesting to obtain a bijective proof.
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…