Bijective proofs of basic hypergeometric series identities
نویسندگان
چکیده
منابع مشابه
Combinatorial proofs of identities in basic hypergeometric series
In this paper, the q–Pfaff-Saalschütz formula and the q–Sheppard 3φ2 transformation formula are established combinatorially.
متن کاملBijective proofs of Gould's and Rothe's identities
We first give a bijective proof of Gould’s identity in the model of binary words. Then we deduce Rothe’s identity from Gould’s identity again by a bijection, which also leads to a double-sum extension of the q-Chu-Vandermonde formula.
متن کاملBijective Proofs of Certain Vector Partition Identities
for 1 <; i < k. L. Carlitz [2] first derived the generating function for restricted bipartite partitions. Subsequently Carlitz and Roselle [3] enumerated certain special families of these partitions e.g., restricted bipartite partitions where the m< and % are all odd. Finally both Roselle [4] and Andrews [1] have obtained different generalizations for multipartite partitions. All these results ...
متن کاملElementary Derivations of Identities for Bilateral Basic Hypergeometric Series
We give elementary derivations of several classical and some new summation and transformation formulae for bilateral basic hypergeometric series. For purpose of motivation, we review our previous simple proof (“A simple proof of Bailey’s very-well-poised 6ψ6 summation”, Proc. Amer. Math. Soc., to appear) of Bailey’s very-well-poised 6ψ6 summation. Using a similar but different method, we now gi...
متن کاملBijective Proofs for Schur Function Identities
In [4], Gurevich, Pyatov and Saponov stated an expansion for the product of two Schur functions and gave a proof based on the Plücker relations. Here we show that this identity is in fact a special case of a quite general Schur function identity, which was stated and proved in [1, Lemma 16]. In [1], it was used to prove bijectively Dodgson’s condensation formula and the Plücker relations, but w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1987
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1987.127.103