Bijective proofs of Gould-Mohanty's and Raney-Mohanty's identities

نویسنده

  • Victor J. W. Guo
چکیده

Using the model of words, we give bijective proofs of Gould-Mohanty's and Raney-Mohanty's identities, which are respectively multivariable generalizations of Gould's identity n k=0 x − kz k y + kz n − k = n k=0 x + ǫ − kz k y − ǫ + kz n − k and Rothe's identity n k=0 x x − kz x − kz k y + kz n − k = x + y n .

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Bijective Proofs for Schur Function Identities which Imply Dodgson's Condensation - Formula and Plu"cker Relations

We exhibit a “method” for bijective proofs for determinant identities, which is based on translating determinants to Schur functions by the Jacobi–Trudi identity. We illustrate this “method” by generalizing a bijective construction (which was first used by Goulden) to a class of Schur function identities, from which we shall obtain bijective proofs for Dodgson’s condensation formula, Plücker re...

متن کامل

Bijective Proofs of Vajda’s Ninetieth Fibonacci Number Identity and Related Identities

This article provides the first bijective proof for a previously “uncounted” Fibonacci number identity of Vajda. Bijections on similar sets that illustrate a related family of Fibonacci number identities are also considered.

متن کامل

Particle Seas and Basic Hypergeometric Series

The author introduces overpartitions and particle seas as a generalization of partitions. Both new tools are used in bijective proofs of basic hypergeometric identities like the q-binomial theorem, Jacobi’s triple product, q-Gauß equality or even Ramanujan’s 1Ψ1 summation. 1. Partitions In 1969, G. E. Andrews was already looking for bijective proofs for some basic hypergeometric identities. The...

متن کامل

Combinatorial Proofs of Some Simons-type Binomial Coefficient Identities

We provide elementary bijective proofs of some curious binomial coefficient identities which were obtained using Cauchy’s integral formula.

متن کامل

Recurrence Relations and Two-Dimensional Set Partitions

In this paper, we consider a two-dimensional model for finite set partitions which arises in conjunction with a special case of a general non-linear recurrence. We investigate properties of some of the related counting sequences, including recurrences and generating functions. In particular, we obtain, by combinatorial arguments, some formulas relating these sequences to the Stirling numbers of...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Ars Comb.

دوره 106  شماره 

صفحات  -

تاریخ انتشار 2012