相关论文: Une identit\'e en th\'eorie des partitions

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.

We translate Uchimura's identity for the divisor function and whose generalizations into combinatorics of partitions, and give a combinatorial proof of them. As a by-product of their proofs, we obtain some combinatorial results.

In this note, we will give a short proof of an identity for cubic partitions.

We present a conjecture about partitions, with a very elementary formulation.

We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression of two shifted symmetric functions, related with Jack…

We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrew's in which he considers the generation function for partitions with respect to size, number of odd parts, and number of…

We prove a partition identity conjectured by Lassalle (Adv. in Appl. Math. 21 (1998), 457-472).

In this work it is propose an alterative proof of one of basic properties of the zonal polynomials. This identity is generalised for the Jack polynomials.

We present a new identity involving compositions (i.e. ordered partitions of natural numbers). The Formula has its origin in complex dynamical systems and appears when counting, in the polynomial family $\{f_c:z \mapsto z^d + c \}$,…

Recently, George Andrews has given a Glaisher style proof of a finite version of Euler's partition identity. We generalise this result by giving a finite version of Glaisher's partition identity. Both the generating function and bijective…

Partitions with distinct even parts have long been the subject of extensive research. In this paper, We present some new perspectives on such partitions from a combinatorial viewpoint, and connect them with signed partitions and bicolored…

Mendes recently conjectured an identity simplifying the Poincar\'e series of the space of equivariant polynomial maps from $\mathbb{R}^{n}$ to a subrepresentation of $Sym^{2}(\mathbb{R}^{n})$. We show how to prove this identity using a…

The G\"ollnitz-Gordon-Andrews identities generalize the partition identities discovered independently by H. G\"ollnitz and B. Gordon. In this article, we present a commutative algebra proof of the G\"ollnitz-Gordon-Andrews identities. More…

We present a simple iteration for the Lebesgue identity on partitions, which leads to a refinement involving the alternating sums of partitions.

We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kur\c{s}ung\"oz. We also present some related polynomial and $q$-series…

Recently Andrews and Bachraoui proved identities relating certain restricted partitions into distinct even parts with restricted 4-regular partitions by the theory of basic hypergeometric series. They also posed a question regarding…

We propose and recursively prove polynomial identities which imply Capparelli's partition theorems. We also find perfect companions to the results of Andrews, and Alladi, Andrews and Gordon involving $q$-trinomial coefficients. We follow…

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…

Euler's classic partition identity states that the number of partitions of $n$ into odd parts equals the number of partitions of $n$ into distinct parts. We develop a new generalization of this identity, which yields a previous…

In this paper, we first give a simple combinatorial proof of Tepper's identity. Then, as a by product of this interesting identity we present another proof of the well-known Wilson's identity in number theory. Finally, we obtain a…