@article {16806,
	title = {Groups of permutations that are even on subsets of a fixed size, and related monoids},
	journal = {International Journal of Algebra and Computation (DOI 10.1142/S0218196725500407; Online 16 October 2025)},
	volume = {36},
	year = {2026},
	pages = {1-15},
	abstract = {<p>In this paper, we study permutations on n elements that are even on every subset of size t. We describe all groups of these permutations. Unexpectedly, these groups (except for some special cases) are either trivial, cyclic or dihedral. In this context, we define and study monoids that generalize both monoids of order-preserving mappings and monoids of orientation-preserving mappings.</p>
},
	url = {https://doi.org/10.1142/S0218196725500407},
	author = {Fernandes, V{\'\i}tor H. and Vernitski, A.}
}
