Title: Ternary and $n$-ary $f$-distributive Structures,
Abstract: We introduce and study ternary $f$-distributive structures, Ternary
$f$-quandles and more generally their higher $n$-ary analogues. A
classification of ternary $f$-quandles is provided in low dimensions. Moreover,
we study extension theory and introduce a cohomology theory for ternary, and
more generally $n$-ary, $f$-quandles. Furthermore, we give some computational
examples.