0
votes
1answer
27 views

Finding the 'n'th k-permutation of a set, and finding 'n' for a given k-permutation (lexicographical ordering)

Suppose you have a set, and want to order the k-permutations of the set (for example, the permutations of 5 elements of the set {1, 2, 3, ..., 16}). Is there a fast way of finding 'n' (the ...
2
votes
2answers
38 views

Algorithm to compute maximum permutation sum in matrix

Given a matrix $A_{n\times n}$ of real numbers, what fast algorithms do there exist to compute the maximum value of $a_{1,\sigma(1)}+a_{2,\sigma(2)}+\ldots+a_{n,\sigma(n)}$ over all permutations ...
1
vote
0answers
16 views

Composing permutations in factorial notation

Given two permutations $p_1$ and $p_2$ in factorial notation, is there a direct algorithm which computes their composition directly, i.e. without translating to a different notation or via computing ...
0
votes
0answers
30 views

Maximum Set Selection Problem

Mike has N different items. He has M orders of customers and each customer has a set of items they want. Customer will not accept partial order. So Mike can give one item to atmost 1 customer. Find ...
0
votes
0answers
38 views

Summing the product of combinations of matrix elements

I have a situation where I have an $NxN$ matrix $A$ where each element $a_{i,j}\in\mathbb{R}_{\leq 0}$. I would like to consider the set of all collections of elements such that each collection of $N$ ...
2
votes
1answer
23 views

Permutation query

Would anyone be able to help here with this one ? Let $A = \{a, …, z, A, …, Z, 0, …, 9\}$ be some alphabet and let $$q = q_1, …, q_m \text{ and } w = w_1, …, w_n$$ be finite-length words in $A^*$. ...
0
votes
1answer
69 views

Alternating Pair

I want to find the number of permutations of $1,2,\ldots,N$ having exactly $k$ triples satisfying the condition that either $n_{i-1}>n_i<n_{i+1}$ or $n_{i-1}<n_i>n_{i+1}.$ For example for ...
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 ...
3
votes
1answer
87 views

Expected Value of this function

Let’s consider a random permutation p1, p2, …, pN of numbers 1, 2, …, N and Function F is calculated as F=(X[2]+…+X[N-1])^K, where ...
1
vote
0answers
231 views

Finding the number of arrangement of N people of different height such that K of them are visible from front

Moderator Note: This is a current contest question on codechef.com. [Initially, I had asked this question in stackoverflow, but someone suggested to post it here, and hence this question is ...
0
votes
2answers
204 views

How do I find the maximum number of knights on a chess board?

I came across this problem and after thinking a lot I could not get any idea how to calculate it. Please suggest to me the right way to calculate it. Given a position where a knight is placed on ...
3
votes
1answer
52 views

How to arrange $n$ pairs of numbers so that this expression is minimized

Consider $n$ pairs of positive integers, $(x_1, y_1), (x_2, y_2), \dots, (x_n, y_n)$. Make a permutation $(a_1, b_1), (a_2, b_2), \dots, (a_n, b_n)$ of these pairs, such that for all $x_i, y_i$, a ...
1
vote
3answers
71 views

Distribute Gifts among students

$N$ students are to be provided with gifts We know that the $i$'th student wants to get at least $a_i$ gifts. The teacher wants to give distinct gifts meaning if he give $x$ gifts to one student then ...
1
vote
0answers
78 views

Permutation for arranging letters in such a way that no similar letters come together (except SPACE)

I would like to get a general expression for arranging n letters such that any similar letters in them never come together (except SPACE). For example : Lets take AABBCCC and three ...
2
votes
3answers
118 views

Divisibility by seven

Given number n, whose decimal representation contains digits only $1, 6, 8, 9$. Rearrange the digits in its decimal representation so that the resulting number will be divisible by 7. If number is m ...
5
votes
1answer
174 views

Numbers permutation

Given $n$ numbers and $k$ positions I want the total number of permutations of these n numbers on these $k$ positions if repetition is allowed and if the following two arrangements are considered ...
0
votes
0answers
15 views

If $A_j=\sum_{x,y,z}B_{x}B_{y}B_{z}$, where $x+y=z+j$, is there a closed form expression for $\frac{\partial A_j}{\partial{B_k}}$?

I am working on a problem involving equations whose interaction is governed by a conservation of momentum condition. Essentially I have two vectors $\mathbf{A}=\left\{A_j\right\}$ and ...
2
votes
1answer
79 views

number of derangements

In the normal derangement problem we have to count the number of derangement when each counter has just one correct house,what if some counters have shared houses. A derangement of n numbers is a ...
1
vote
0answers
61 views

number of ways to arrange

There are N 1s and N 0s We have to arrange them in a row such that at no position in this row the number of 0s from the beginning exceed the number of 1s from the beginning. Also the number of ...
2
votes
2answers
118 views

Maximum number of seating plans

15 people will be seat in a row of 15 chairs. Two seating plan are considered the same if two plans share same adjacent quadruples. What is the maximum number of seating plans can be made? For ...
0
votes
0answers
58 views

How is the algorithm for recursively printing permutations of a set of numbers this equation our professor gave us?

I'm having a great amount of trouble understanding where my prof got $T(m, n) = n(T(m+1, n-1) + m+1 + n)$ if $n > 1$ as the recursive formula for the algorithm for recursively printing the ...
2
votes
4answers
420 views

distributing z different objects among k people almost evenly

We have z objects (all different), and we want to distribute them among k people ( k < = z ) so that the distribution is ...
1
vote
0answers
30 views

Finding k-d sum for all numbers upto maxVal [duplicate]

a number n is a k-d number if either of the following holds true: a) number of digits <=k b) sum of first k digits is equal ...
0
votes
2answers
76 views

Determine no of combinations for cutting stock algorithm

I have to buy $n$ wooden logs of size 2000 each, from which I have to cut different pieces of smaller size say: 255*10 750*7 550*13 In a manner that cutting will ...
0
votes
1answer
75 views

Explanation on step $\rho$ of the SHA-3 algorithm

I'm working on implementing SHA-3 in a PIC microcontroller. In the block permutation, I don't quite understand step $\rho$: Bitwise rotate each of the 25 words by a different triangular number 0, ...
1
vote
1answer
99 views

Minimum number of moves to convert a list of any integers into a permutation

Given a list of integers of size n, how to find the minimum number of moves to convert it to a Permutation? In one move, we are allowed to decrease or increase any element of the list by one. For ...
0
votes
0answers
112 views

Generating a random derangement

I'm having a problem about derangements that I'm trying to solve. Given a set $S = \{1,\ldots,n\}$, I want to generate a random derangement. I've considered generating a permutation and checking ...
5
votes
1answer
184 views

Algorithm creating subsets with certain properties

I'm trying so solve following problem: Let's say, we have a set $A=\{1,2,3,...,49\}$. Now, I am defining sets $A_1, A_2, A_3,...,A_n$ as follow: $A_1=\{a_1,a_2,a_3,...,a_{30}\}$, $A_2= ...
30
votes
1answer
1k views

Is War necessarily finite?

War is an cardgame played by children and drunk college students which involves no strategic choices on either side. The outcome is determined by the dealing of the cards. These are the rules. A ...
1
vote
0answers
154 views

Who invented the breadth-first permutation algorithm?

My initial problem was solved here. It is about enumerating all n-tuples of a permutation in a specific order. The solution algorithm is very simple and I'm sure has been used before. However, I did ...
2
votes
1answer
109 views

How to find a canonical member of an equivalence class of matrices under row and column swaps?

Call two matrices "swap-equivalent" if one matrix can be transformed into the other via some sequence of row swaps and column swaps. I'd like a computationally efficient algorithm that can transform ...
3
votes
1answer
286 views

How many non-isomorphic permutation selections are on an arbitrary N x N square matrix with rotations applied?

My question is an extension to a classic one: On a square $N \times N$ grid, select exact $N$ cells that satisfy condition: only one cell selected in same row and column. How many solutions will ...
-2
votes
1answer
161 views

How many possible ways are there

Suppose i have the given data set of length 11 of scores p=[2, 5, 1 ,2 ,4 ,1 ,6, 5, 2, 2, 1] I want to select 6 ,5 , 5 , 4 , 2 , 2 scores from the data set. How many ways are there? For the above ...
0
votes
0answers
74 views

Calculate pairing in a rotational system

I'm not even sure how to word this question. So I'll explain it out. I've got these values: A1, A2, B1, B2, B3, C1, C2, I need each A to be paired with each B and C each B with each A and C ...
7
votes
1answer
363 views

Algorithm for scrolling through different orbits in a permutation group

Given an $n\in\mathbb{N}$, and a permutation $\pi\in S_{n}$, denote the centralizer of $\pi$ by $C_{\pi}$. Now we can look on the conjugation action of $C_{\pi}$ on $S_{n}$ and then divide $S_{n}$ to ...
17
votes
3answers
3k views

How does one compute the sign of a permutation?

The sign of a permutation $\sigma\in \mathfrak{S}_n$, written ${\rm sgn}(\sigma)$, is defined to be +1 if the permutation is even and -1 if it is odd, and is given by the formula $${\rm sgn}(\sigma) ...
1
vote
1answer
142 views

Question on permutation

I asked this question : Composition of permutation to generate all permutations earlier but I didn't phrase it well, here is my new question. My question is a little bit different I'm looking for a ...
4
votes
3answers
735 views

Composition of permutation to generate all permutations

Looking at permutations I came up with the following question: Can you find a permutation S of a set of n elements such that by composing this permutation n! times you will describe all the possible ...
4
votes
1answer
393 views

Is it possible to efficiently factor a semiprime given a bit-permutation relating the factors?

Is it possible to efficiently factor a semiprime given a bit-permutation relating the factors? For example, suppose we have $n = p * q = 167653$; in this case, $p = 359 = 101100111_2$ and $q = 467 = ...
1
vote
0answers
213 views

Anti-prime sequence

I have permutation from $x$ to $y$. And how to make sequence which $d$ summed numbers from this sequence ISN'T a prime number. if we have sequence $x_1,x_2,x_3,x_4,x_5 \dots y$ than $d$ means : ...
2
votes
4answers
166 views

Is this a kind of Permutation?

I'm trying to design an algorithm to generate something that I don't know how exactly to call! Ok, I'm not a mathematician, I'm studying computer science and thought this would be a great moment to ...
1
vote
6answers
631 views

Why is the number of possible subsequences $2^n$?

If anyone here is familiar with the Lowest Common Subsequence problem, they probably know that the number of posibble subsequences in a sequence is $2^n$; $n$ being the length of the sequence. ...
3
votes
2answers
1k views

Can someone explain the algorithm for composition of cycles?

Let $\sigma=(1\ 3),\ \tau=(2\ 4\ 5),\ \pi=(2\ 3\ 4) \in S_{5}$. Find $\pi\circ\tau\circ\sigma$. I know the solution is $(1\ 4\ 5\ 3)$. What i'm doing now is writing the permutations in the ...
4
votes
1answer
950 views

Finding all n×n permutation matrices

If I have a doubly stochastic matrix, how can I find the set of all basic feasible solutions? Here's Wikipedia on doubly stochastic matrices.