Linear-Time and Constant-Space Algorithms to compute Multi-Sequences that arise in Enumerative Combinatorics (and Elsewhere)
Combinatorics
2022-03-11 v1
Abstract
How many ways, exactly, can a Chess King, always moving forward (i.e. with steps [1,0],[0,1],[1,1]) walk to [100000,200000]? Thanks to the amazing Apagodu-Zeilberger extension of the Almkvist-Zeilberger algorithm, adapted in this article for combinatorial applications, this 104492-digit number, can be computed in less than 33 seconds. But not just this particular number. Many other numbers that come up in enumerative combinatorics, can be computed just as efficiently
Cite
@article{arxiv.2203.04966,
title = {Linear-Time and Constant-Space Algorithms to compute Multi-Sequences that arise in Enumerative Combinatorics (and Elsewhere)},
author = {Shalosh B. Ekhad and Doron Zeilberger},
journal= {arXiv preprint arXiv:2203.04966},
year = {2022}
}
Comments
4 pages. Accompanied by Maple packages and output files available from https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/pure.html