36 citations · 41 across the 9 of their papers we have counts for
9 papers · 1 filter
The Generating Function of Ternary Trees and Continued Fractions
Ira Gessel, Guoce Xin
Michael Somos conjectured a relation between Hankel determinants whose entries count ternary trees and the number of certain plane partitions and alterna…
A Short Proof of the Zeilberger-Bressoud -Dyson Theorem
Ira M. Gessel, Guoce Xin
We give a formal Laurent series proof of Andrews's -Dyson Conjecture, first proved by Zeilberger and Bressoud.
Constructing All Magic Squares of Order Three
Guoce Xin
We find by applying MacMahon's partition analysis that all magic squares of order three, up to rotations and reflections, are of two types, each generated by three basis elements.…
Counting Lattice Paths By Gessel Pairs
Guoce Xin
We count a large class of lattice paths by using factorizations of free monoids. Besides the classical lattice paths counting problems related to Catalan numbers, we give a new app…
A Residue Theorem for Malcev-Neumann Series
Guoce Xin
In this paper, we establish a residue theorem for Malcev-Neumann series that requires few constraints, and includes previously known combinatorial residue theorems as special cases…
A Fast Algorithm for MacMahon's Partition Analysis
Guoce Xin
This paper deals with evaluating constant terms of a special class of rational functions, the Elliott-rational functions. The constant term of such a function can be read off immed…