4 citations · 5 across the 6 of their papers we have counts for
7 papers
Graded automorphisms of quantum affine spaces
Hai Jin
This paper computes the graded automorphism group of quantum affine spaces. Specifically, we determine that this group is isomorphic to a semi-direct product of a blocked diagonal…
Congruences on the Number of Restricted -ary Partitions
Qing-Hu Hou, Hai-Tao Jin, Yan-Ping Mu +1
Andrews, Brietzke, Rødseth and Sellers proved an infinite family of congruences on the number of the restricted -ary partitions when is a prime. In this note, we show that t…
Ramanujan-type Congruences for -Regular Partitions Modulo and
Hai-Tao Jin, Li Zhang
Let be the number of -regular partitions of . Recently, Hou et al established several infinite families of congruences for modulo , where $(\ell…
Abel's Lemma and Identities on Harmonic Numbers
Hai-Tao Jin, Daniel K. Du
Recently, Chen, Hou and Jin used both Abel's lemma on summation by parts and Zeilberger's algorithm to generate recurrence relations for definite summations. Meanwhile, they propos…
On the Number of Partitions with Designated Summands
William Y. C. Chen, Kathy Q. Ji, Hai-Tao Jin +1
Andrews, Lewis and Lovejoy introduced the partition function PD(n) as the number of partitions of with designated summands, where we assume that among parts with equal size, ex…
Formal residue and computer proofs of combinatorial identities
Qing-Hu Hou, Hai-Tao Jin
The coefficient of x^{-1} of a formal Laurent series f(x) is called the formal residue of f(x). Many combinatorial numbers can be represented by the formal residues of hypergeometr…
The Abel-Zeilberger Algorithm
William Y. C. Chen, Qing-Hu Hou, Hai-Tao Jin
We use both Abel's lemma on summation by parts and Zeilberger's algorithm to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case…