5 papers
On the Summability Problem of Multivariate Rational Functions in the Mixed Case
Shaoshi Chen, Lixin Du, Hanqian Fang +1
Continuing previous work, this paper focuses on the summability problem of multivariate rational functions in the mixed case in which both shift and -shift operators can appear.…
Automated Formal Proofs of Combinatorial Identities via Wilf-Zeilberger Guidance and LLMs
Beibei Xiong, Hangyu Lv, Junqi Liu +5
Automating formal proofs of combinatorial identities is challenging for LLM-based provers, as long-horizon proof planning is required and unconstrained search quickly explodes. Sym…
Symbolic Integration of Differential Forms: From Abel to Zeilberger
Shaoshi Chen, David A. Cox, Yisen Wang
This paper focuses on symbolic integration of differential forms, with a particular emphasis on historical and modern developments, from Abel's addition theorems for Abelian integr…
How to generate all possible rational Wilf-Zeilberger forms?
Shaoshi Chen, Christoph Koutschan, Yisen Wang
Wilf-Zeilberger pairs are fundamental in the algorithmic theory of Wilf and Zeilberger for computer-generated proofs of combinatorial identities. Wilf-Zeilberger forms are their hi…
Non-minimality of minimal telescopers explained by residues
Shaoshi Chen, Manuel Kauers, Christoph Koutschan +3
Elaborating on an approach recently proposed by Mark van Hoeij, we continue to investigate why creative telescoping occasionally fails to find the minimal-order annihilating operat…