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...

Many games display some kind of material symmetry. That is, some sets of game elements can be exchanged for another set of game elements, so that the resulting position will be equivalent to the original one, no matter how the elements were arranged on the board. Material symmetry is routinely used in card game engines when they normalize their internal representation of the cards. Other games ...

On the one hand, we prove that the spaces of C 1 symplectomor-phisms and of C 1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On the other hand, we show that the space of C 1 diffeomorphisms of the circle and a non-empty open set of C 1 diffeomorphisms of the two-sphere contain dense subsets of diffeomorphisms whose centralize...

An integral square matrix A is called principally unimodular (PU if every nonsingular principal submatrix is unimodular (that is, has determinant \1). Principal unimodularity was originally studied with regard to skew-symmetric matrices; see [2, 4, 5]; here we consider symmetric matrices. Our main theorem is a generalization of Tutte's excluded minor characterization of totally unimodular matri...