PreprintarXiv licencearXiv
Higher-dimensional generalized quasiorders
Abstract
It is well known that the polymorphism clone of a quasiorder is determined by its unary part, in the sense that any operation is a polymorphism if it satisfies the condition that all unary functions obtained by fixing some of its variables at constant values are polymorphisms. We show that a clone satisfies an analogous property for a particular fixed arity d if and only if it is determined by a collection of what we call higher-dimensional generalized quasiorders whose dimension is equal to d. We define higher-dimensional generalized quasiorders with the appropriate generalizations of reflexivity and transitivity to the higher-dimensional setting, which rely on an explicit analysis of 'rectangular' arity.
Related
- Higher-dimensional Golden Section, Generalized Fibonacci Sequence, and Multiple Online Leasing
- Higher order Teodorescu transform in the theory of generalized partial-slice monogenic functions
- Higher Integrability, Generalized Symmetries, and Partially Topological Field Theories
- A higher order family of iterative methods for approximating inverse and generalized inverse matrices
- Asymptotically Tight Bounds for Generalized Covering Radii of Binary Primitive BCH Codes at All Higher Orders
BibTeX
@misc{moorhead2026higherdimensional,
title = {{Higher-dimensional generalized quasiorders}},
author = {Andrew Moorhead and Reinhard Pöschel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07339},
eprint = {2609.07339},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07339},
}
RIS
TY - UNPB
TI - Higher-dimensional generalized quasiorders
AU - Andrew Moorhead
AU - Reinhard Pöschel
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07339
UR - https://arxiv.org/abs/2609.07339
AB - It is well known that the polymorphism clone of a quasiorder is determined by its unary part, in the sense that any operation is a polymorphism if it satisfies the condition that all unary functions obtained by fixing some of its variables at constant values are polymorphisms. We show that a clone satisfies an analogous property for a particular fixed arity d if and only if it is determined by a collection of what we call higher-dimensional generalized quasiorders whose dimension is equal to d. We define higher-dimensional generalized quasiorders with the appropriate generalizations of reflexivity and transitivity to the higher-dimensional setting, which rely on an explicit analysis of 'rectangular' arity.
ER -