منابع مشابه
On Distinct Consecutive Differences
We show that if A = {a1, a2, . . . , ak} is a monotone increasing set of numbers, and the differences of the consecutive elements are all distinct, then |A+B| ≥ c|A|1/2|B| for any finite set of numbers B. The bound is tight up to the constant multiplier.
متن کاملDistinct Fuzzy Subgroups of a Dihedral Group of Order $2pqrs$ for Distinct Primes $p, , q, , r$ and $s$
In this paper we classify fuzzy subgroups of the dihedral group $D_{pqrs}$ for distinct primes $p$, $q$, $r$ and $s$. This follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.We present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...
متن کاملCyclic sequences of k-subsets with distinct consecutive unions
In this paper, we investigate cyclic sequences which contain as elements all k-subsets of {0, 1, . . . , n−1} exactly once such that the unions of any two consecutive k-subsets of this sequences are pairwise distinct. Furthermore, if Y is some prescribed subset of the power set of {0, 1, . . . , n− 1}, we require that all unions are in Y . In particular, we are interested in the case where Y co...
متن کاملdistinct fuzzy subgroups of a dihedral group of order $2pqrs$ for distinct primes $p, , q, , r$ and $s$
in this paper we classify fuzzy subgroups of the dihedral group $d_{pqrs}$ for distinct primes $p$, $q$, $r$ and $s$. this follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.we present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...
متن کاملOn Consecutive Integer Pairs with the Same Sum of Distinct Prime Divisors
We define the arithmetic function P by P (1) = 0, and P (n) = p1 + p2 + · · ·+ pk if n has the unique prime factorization given by n = ∏k i=1 p ai i ; we also define ω(n) = k and ω(1) = 0. We study pairs (n, n+ 1) of consecutive integers such that P (n) = P (n+ 1). We prove that (5, 6), (24, 25), and (49, 50) are the only such pairs (n, n + 1) where {ω(n), ω(n + 1)} = {1, 2}. We also show how t...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2019
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2018.11.018