1
vote
1answer
52 views

Finding Required Permutation

I have numbers from $1$..$n$. I want to find number of permutation from all $n!$ permutation where the numbers have following arrangement. $L$ $G$ $L$ $G$ $L$ or $G$ $L$ $G$ $L$ $G$. Where L means ...
0
votes
0answers
36 views

Removing the Summation (Closed Form)

The following question from "Combinatorics of Permutations" : $$ E[X] = \sum\limits_{k = 2}^n \frac{k\cdot T(n,k)}{n!} $$ where $$ T(n,k) = k \cdot T(n-1, k) + 2 \cdot T(n-1, k-1) + (n-k) \cdot ...
0
votes
1answer
100 views

Hypothesis testing for equivalence of two arrangements

I have two arrangements(i.e. permutations) of numbers. First one is the target/real arrangement. Second, is the observed arrangement. e.g. Target := 1,2,3,4,5,6,7 Observed := ...
1
vote
1answer
53 views

Sum to infinite terms faster method

Finding sum to infinite terms of series: $$\frac{1}{1\cdot3\cdot5} + \frac{1}{3\cdot5\cdot7} + \frac{1}{5\cdot7\cdot9} + \cdots$$ I approached this question by writing the general term first,then ...
2
votes
1answer
47 views

permuting digits of a number

Given a number $N$ with upto 18 digits, We need to find how many numbers smaller than $N$ can be formed using the same digits. Eg: for 725 we can form 527,572,257,275 hence answer=4
0
votes
1answer
99 views

What is this the name of this idea? (combinatorics)

The problem: There are three screws, each one a different type {Phillips, Robinson, Slotted}. There are three sets of screwdrivers, each set corresponds to a type of screw. There are no two ...
4
votes
0answers
69 views

Selecting k numbers out of N sorted numbers to a minimize a condition/Formula

A sorted list of $\mathbf N$ numbers is given. $X_1$ $\le$ $X_2$ $\le$ $X_3$ $\le$ .... $\le$ $X_N$ Select $\mathbf K$ Numbers - $Y_1$ , $Y_2$ , $Y_3$ , ..... , $Y_K$ - Such that the following ...
2
votes
0answers
109 views

Getting K heads out of N biased coins problem (formula generation ).

Problem- Given a set of coins n with each coin i having Pi probability to give heads. Find the probability of getting k heads, when all coins are tossed together. hi i have solved this problem ...
2
votes
1answer
40 views

How many increasing 3 term geometric progressions can be obtained from the sequence $1, 2, 2^2,2^3,… …, 2^n$?

For example, an increasing 3-term geometric progression for $n ≤ 8$ is $\{2^2, 2^5, 2^8\}$.
2
votes
0answers
172 views

Is it possible to find sum of this series?

I am trying to find the sum of the following series asked by my friend. $$n\cdot\left(\bigl\lfloor\tfrac{n}{2}\bigr\rfloor+ \bigl\lfloor\tfrac{n}{3}\bigr\rfloor+ \bigl\lfloor\tfrac{n}{4}\bigr\rfloor+ ...
1
vote
1answer
178 views

Equation to find possible combinations of combining lists while retaining order

Lets say I have two ordered lists of size n, [A1, A2, ..., An] and [B1, B2, ...,Bn]. I want to find all the possible ...
1
vote
0answers
57 views

Matrix Representation of Integer Series

I would like some feedback regarding this process or the meaning of this process. Let say that I have a discrete time series: S = [1 2 3 4 5] And that I represent this serie by a stochastic matrix M ...
4
votes
3answers
347 views

Summation of a finite series involving permutations.

$$\large \sum_{i = 2}^{25}P(i,2)$$ $P$ stands for "permutations".
3
votes
3answers
267 views

How to get the N-th word in a sequence

Suppose I have an alphabet (e.g. consisting of ABCDEF) and a lexicographic order is defined i.e. A -> B ... -> F -> AA -> AB .. -> AF -> BA -> BB -> ... -> BF ... -> FF -> AAA -> ... Is there a ...
2
votes
2answers
76 views

Can two finite sequences be considered permutations if their products and sums are equal?

Given two finite ordered sequences with possibly non-unique elements all greater than one: $A,B \in \mathcal{Z}_{>1}$. Given that we have: \begin{eqnarray} |A| &= |B| \\ \Pi_{x \in ...
11
votes
1answer
492 views

Shortest sequence containing all permutations

Given an integer $n$, define $s(n)$ to be the length of the shortest sequence $S = (a_1, \cdots a_{s(n)})$ such that every permutation of $\{1,\cdots,n\}$ is a subsequence of $S$. If $n=1$, then $S = ...