The Cardinality of Some Symmetric Differences
نویسندگان
چکیده
In this paper, we prove that for positive integers k and n, the cardinality of the symmetric differences of {1, 2, . . . , k}, {2, 4, . . . , 2k}, {3, 6, . . . , 3k}, . . . , {n, 2n, . . . , kn} is at least k or n, whichever is larger. This solved a problem raised by Pilz in which binary composition codes were studied.
منابع مشابه
Symmetric Cardinality Constraint with Costs
The symmetric cardinality constraint is described in terms of a set of variables X = {x1, . . . , xk}, which take their values as subsets of V = {v1, . . . , vn}. It constraints the cardinality of the set assigned to each variable to be in an interval [lxi , uxi ] and at the same time it restricts the number of occurrences of each value vj ∈ V in the sets assigned to variables in X to be in an ...
متن کاملSome results on the symmetric doubly stochastic inverse eigenvalue problem
The symmetric doubly stochastic inverse eigenvalue problem (hereafter SDIEP) is to determine the necessary and sufficient conditions for an $n$-tuple $sigma=(1,lambda_{2},lambda_{3},ldots,lambda_{n})in mathbb{R}^{n}$ with $|lambda_{i}|leq 1,~i=1,2,ldots,n$, to be the spectrum of an $ntimes n$ symmetric doubly stochastic matrix $A$. If there exists an $ntimes n$ symmetric doubly stochastic ...
متن کاملStock Portfolio-Optimization Model by Mean-Semi-Variance Approach Using of Firefly Algorithm and Imperialist Competitive Algorithm
Selecting approaches with appropriate accuracy and suitable speed for the purpose of making decision is one of the managers’ challenges. Also investing decision is one of the main decisions of managers and it can be referred to securities transaction in financial markets which is one of the investments approaches. When some assets and barriers of real world have been considered, optimization of...
متن کاملAutomorphism Group of a Possible 2-(121, 16, 2) Symmetric Design
Let D be a symmetric 2-(121, 16, 2) design with the automorphism group of Aut(D). In this paper the order of automorphism of prime order of Aut(D) is studied, and some results are obtained about the number of fixed points of these automorphisms. Also we will show that |Aut(D)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. In addition we prese...
متن کاملSome vector fields on a riemannian manifold with semi-symmetric metric connection
In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.
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 2009