polygroups are multivalued systems that satisfy group like axioms. in this paper the class of n-arypolygroups is introduced. the concepts of n-ary normal subpolygroups and strong homomorphisms of n-arypolygroups are adopted. with respect to these concepts the isomorphism theorems for n-ary polygroups arestated and proved. finally, we will consider the fundamental relation  * defined on an n-ar...

in this paper the class of n-ary hypergroups is introduced and several properties are found andexamples are presented. n-ary hypergroups are a generalization of hypergroups in the sense of marty. on theother hand, we can consider n-ary hypergroups as a good generalization of n-ary groups. we define thefundamental relation β* on an n-ary hypergroup h as the smallest equivalence relation such tha...

In this paper, we introduce the concept of fuzzy congruences on n-ary semigroups and describe quotient n-ary semigroups by fuzzy congruences. Some isomorphism theorems about n-ary semigroups are established. Moreover, we discuss a special kind of n-ary semigroups. We also establish relationships between normal fuzzy ideals and fuzzy congruences. In particular, we prove that there exists a prese...

The notion of an n-ary group is a natural generalization of the notion of a group and has many applications in different branches. In this paper, the notion of (normal) fuzzy n-ary subgroup of an n-ary group is introduced and some related properties are investigated. Characterizations of fuzzy n-ary subgroups are given.

The class of  $n$-ary polygroups is a certain subclass of $n$-ary hypergroups, a generalization of D{"o}rnte $n$-arygroups and  a generalization of polygroups. The$beta^*$-relation and the $gamma^*$-relation are the smallestequivalence relations on an $n$-ary polygroup $P$ such that$P/beta^*$ and $P/gamma^*$ are an $n$-ary group and acommutative $n$-ary group, respectively. We use the $beta^*$-...

We study fringe subtrees of random m-ary search trees and of preferential attachment trees, by putting them in the context of generalised Pólya urns. In particular we show that for the random m-ary search trees with m ≤ 26 and for the linear preferential attachment trees, the number of fringe subtrees that are isomorphic to an arbitrary fixed tree T converges to a normal distribution; more gene...

In this paper, we have generalized the definition of vector space by considering the group as a canonical $m$-ary hypergroup, the field as a krasner $(m,n)$-hyperfield and considering the multiplication structure of a vector by a scalar as hyperstructure. Also we will be consider a normed $m$-ary hypervector space and introduce the concept of convergence of sequence on $m$-ary hypernormed space...