Counting Baxter matrices
The electronic journal of combinatorics, Tome 30 (2023) no. 1
Donald Knuth recently introduced the notion of a Baxter matrix, generalizing Baxter permutations. We show that for fixed number of rows, $r,$ the number of Baxter matrices with $r$ rows and $k$ columns eventually satisfies a polynomial in $k$ of degree $2r-2$. We also give a proof of Knuth's conjecture that the number of 1s in an $r \times k$ Baxter matrix is less than $r+k$.
@article{10_37236_10839,
author = {George Spahn},
title = {Counting {Baxter} matrices},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {1},
doi = {10.37236/10839},
zbl = {1505.05017},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10839/}
}
George Spahn. Counting Baxter matrices. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/10839
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