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Suppose there is a basket $ S$ containing $ 3\ \color{blue}{blue}$ , $ 2\ \color{green}{green}$ and $ 1\ \color{red}{red}$ balls. A subject can extract any $ k$ number of balls (including $ 0$ ) at random from the basket. How many combinations $ C$ there are for each extraction of $ k$ balls? I can’tRead more

I need mathematical express for how many combinations of input arrays create same Binary Max-Heap when we put values one by one from array using method Insert. Example: Final heap This heap are represent by this array [9, 7, 8, 6, 4, 2, 4, 1, 5]. If we create new heap and we start puttingRead more

For example there’s a table which has only boolean fields and 1 id key, there is any sql query (in my case for Microsoft SQL Server) that is able to fulfill such table with all of the possible combination of these bool fields? Let put it’s a 3 column boolean + id key, so 2^(3)Read more

This question is contains a revised conjecture to a conjecture I posed previously which was shown to be false. Let $ p, q \in \mathbb{C}[t]$ be two monic polynomials of degree $ n \ge 1$ . For $ \alpha \in [0,1]$ , let $ $ c_\alpha := \alpha p + (1-\alpha)q \in \mathbb{C}[t]$ $ SinceRead more

I have following lists: list1={1,2,3,4,5} and list2={10,20,30,40,50} I want to combine these lists such that each element in list1 is added to every element in list2, to form the list3 as list3={1+10,1+20,1+30,1+40,1+50,2+10,2+20,2+30,2+4=,2+50,…5+10,5+20,5+30,5+40,5+50} How can this be done efficiently using Mathematica?Read more

I have an algorithm that creates a graph that has all representations of 4-bit binary strings encoded in the form of the shortest graph paths, where an even number in the path means 0, while an odd number means 1: from itertools import permutations, product import networkx as nx import matplotlib.pyplot as plt import progressbarRead more

I found an interesting question on quora and need help in solving this question. I’ve just started understanding permutations but could not understand as to how I can come up with a general formula for this problem. Consider all permutations of the numbers 1 to n. A good permutation is one where for any numberRead more

Since some days, I’m trying to simplify a recursive and long algorithm into a fast (non recursive) equation taking 3 parameters into account. I want to precise that I don’t know really how to specify my problem in one question (I don’t know well mathematical combinatorials vocabulary). I will try to be as much understandableRead more

Let $ M$ be a finitely generated abelian group. Assume we are given a presentation of $ M$ , that is \begin{equation*} M = \frac{\bigoplus_{i=1}^r \mathbf{Z}g_i}{\sum_{j=1}^s \mathbf{Z} r_j} \end{equation*} where the $ g_i$ are the generators and the $ r_j$ are the relations. Let $ x$ be an element of $ M$ , given asRead more

I have a circumstance where I need to create every single possible version of an object upon a particular magnitude. After this, a process occurs which determines the best combination of values at this magnitude and then sets these for the next iteration of the magnitude reduction loop. double bestVal1 = 5, bestVal2 = 5,Read more