Year: 2026
Type: preprint
Abstract: Agustín-Aquino solved, in terms of the table of marks of $\Aff(\mathbb{Z}/2k\mathbb{Z})$, the problem of enumerating the classes of bicolour self-complementary and rigid patterns in $\mathbb{Z}/2k\mathbb{Z}$ (also known as \emph{strong dichotomy classes}). In particular, the rigid pattern-inventory polynomial appeared, for odd $k$, to yield the number of strong classes with negative sign when evaluated in $-1$, and it was conjectured that this is true for $k$ a power of an odd prime. Here we prove the conjecture is true for $k$ odd in general.
Source: arXiv (Cornell University)
Author: Agustín-Aquino, Octavio A.
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162104196
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