Successively orthogonal systems of k - ary operations
نویسندگان
چکیده
Systems of k-ary operations, k > 2, generalizing orthogonal sets are considered. These systems have the following property: every k successive k-ary operations of the system are orthogonal. We call these systems successively orthogonal, establish some properties, give examples and methods of construction of these systems.
منابع مشابه
Secret-sharing schemes and orthogonal systems of k-ary operations
We suggest a general method of the construction of secret-sharing schemes based on orthogonal systems of partial (in particular, everywhere determined) k-ary operations which generalizes some known methods of the construction of such schemes by a nite elds and point the orthogonal systems of k-ary operations respecting to these known schemes. The di erent transformations of orthogonal systems o...
متن کاملON CONSTRUCTION OF ORTHOGONAL d-ARY OPERATIONS
A d-hypercube of order n is an n × · · · × nd (d times) array with n elements from a set Q of cardinality n. We recall several connections between d-hypercubes of order n and d-ary operations of order n. We give constructions of orthogonal d-ary operations that generalize a result of Belyavskaya and Mullen. Our main result is a general construction of d-orthogonal d-ary operations from d-ary qu...
متن کاملQuotient G-systems and Green\'s Relations
In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups . Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper.
متن کاملPolynomial k - ary operations , matrices , and k - mappings
We establish connection between product of two matrices of order k × k over a field and the product of the k-mappings corresponding to the k-operations, defined by these matrices. It is proved that, in contrast to the binary case, for arity k ≥ 3 the components of the k-permutation inverse to a k-permutation, all components of which are polynomial k-quasigroups, are not necessarily k-quasigroup...
متن کاملBranches in random recursive k-ary trees
In this paper, using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. We also find the expectation of the number of nodes of a given outdegree in a branch of such trees.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014