We consider the Minkowski sum of subsets of integer lattice, each of which is a set of integer points of a face of an extended submodular [Kashiwabara-Takabatake, Discrete Appl. Math. 131 (2003) 433] integer polyhedron supported by a common positive vector. We show a sufficient condition ...
Cameron [9] described an algorithm to identify sum-free subsets of positive integers. As he put it, when examining a number a, if this is not the sum of two elements of a set S, then choose uniformly at random whether to put a in S. This informal description does not clarify how a...
Given an array of sizenn. How can we find sum of XOR sum of all subsets in better thanO(2n)O(2n)? For example considerarray=[1,4,5]array=[1,4,5] Answer = 1 + 4 + 5 + 1^4 + 1^5 + 4^5 + 1^4^5Answer = 1 + 4 + 5 + 1^4 + 1^5 + 4^5 + 1^4^5(here '^...
用3sat-证明-subset-sum-是np-complete CMPSCI611:The SUBSET-SUM Problem Lecture18 We begin today with the problem we didn’t get to at the end of last lecture–the SUBSET-SUM problem,which we also saw back in Lecture8.The input to SUBSET-SUM is a set of numbers{a1,...,a n}and a...
Here are examples of what you would use COUNT for:以下是将COUNT⽤于以下⽤途的⽰例：Counting all rows in a table (no group by required)计算表中的所有⾏(不需要按组)Counting the totals of subsets of data (requires a Group By section of the statement)计算数据⼦集的总数(需要语句的“...
The Stirling numbers of the second kind, or Stirling partition numbers, describe the number of ways a set with n elements can be partitioned into k disjoint, non-empty subsets. Common notations are S (n, k) and,-. The study is finalized with an extraordinary identity between the second ...
A finite set $A \\\subset \\\mathbb{Z}$ is considered sum-dominant if $|A+A|>|A-A|$. If we consider all subsets of ${0, 1, ..., n-1}$, as $no\\\infty$ it is natural to expect that almost all subsets should be difference-dominant, as addition is commutative but subtrac...
We derive that, on a four-letter alphabet, the number of Abelian square-free words of eac... A Carpi - 《Discrete Applied Mathematics》 被引量: 67发表: 1998年 The number of maximal sum-free subsets of integers Cameron and Erd艖s raised the question of how many maximal sum-free sets ...
We then give two applications of these results. Our first application allows us to write down a formula for the number of orbits under the natural action ofAut(G)on the set of sum-free subsets ofGof the largest cardinality whenGis of the form(Z/mZ)r, with all prime divisors ofm...
3.To add some set of numbers together:The teacher challenged the students to sum up the numbers from 1 to 100 as fast as possible. I wrote down all of our expenses for the week and summed them up. 4.To calculate something, especially by addition:We need to sum up our total costs fo...