Recent questions tagged combinatory - GATE Overflow

+2 votes

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1

Counting number of pairs whose sum is less than k
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.

asked Jun 9 in Combinatory by dd | 207 views

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2

Kenneth Rosen Edition 7th Exercise 6.6 Question 16 (Page No. 439)
The remaining exercises in this section develop another algorithm for generating the permutations of $\{1, 2, 3,\dots,n\}.$ This algorithm is based on Cantor expansions of integers. Every nonnegative integer less than $n!$ ... between Cantor expansions and permutations as described in the preamble to question $14.$ $3$ $89$ $111$

asked May 2 in Combinatory by Lakshman Patel RJIT | 20 views

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3

Kenneth Rosen Edition 7th Exercise 6.6 Question 17 (Page No. 438)
The remaining exercises in this section develop another algorithm for generating the permutations of $\{1, 2, 3,\dots,n\}.$ ... permutations of a set of n elements based on the correspondence described in the preamble to question $14.$

asked May 2 in Combinatory by Lakshman Patel RJIT | 9 views

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0 answers

4

Kenneth Rosen Edition 7th Exercise 6.6 Question 15 (Page No. 438)
Show that the correspondence described in the preamble is a bijection between the set of permutations of $\{1, 2, 3,\dots,n\}$ and the nonnegative integers less than $n!.$

asked May 2 in Combinatory by Lakshman Patel RJIT | 7 views

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5

Kenneth Rosen Edition 7th Exercise 6.6 Question 14 (Page No. 438)
The remaining exercises in this section develop another algorithm for generating the permutations of $\{1, 2, 3,\dots,n\}.$ This algorithm is based on Cantor expansions of integers. Every nonnegative integer less than $n!$ has a unique ... $a_{1}, a_{2},\dots,a_{n−1}$ that correspond to these permutations. $246531$ $12345$ $654321$

asked May 2 in Combinatory by Lakshman Patel RJIT | 10 views

0 votes

1 answer

6

Kenneth Rosen Edition 7th Exercise 6.6 Question 13 (Page No. 438)
List all $3$-permutations of $\{1, 2, 3, 4, 5\}.$

asked May 2 in Combinatory by Lakshman Patel RJIT | 16 views

0 votes

1 answer

7

Kenneth Rosen Edition 7th Exercise 6.6 Question 12 (Page No. 438)
Develop an algorithm for generating the $r$-permutations of a set of $n$ elements.

asked May 2 in Combinatory by Lakshman Patel RJIT | 9 views

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8

Kenneth Rosen Edition 7th Exercise 6.6 Question 11 (Page No. 438)
Show that Algorithm $3$ produces the next larger $r$-combination in lexicographic order after a given $r$-combination.

asked May 2 in Combinatory by Lakshman Patel RJIT | 8 views

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9

Kenneth Rosen Edition 7th Exercise 6.6 Question 10 (Page No. 438)
Show that Algorithm $1$ produces the next larger permutation in lexicographic order.

asked May 2 in Combinatory by Lakshman Patel RJIT | 7 views

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0 answers

10

Kenneth Rosen Edition 7th Exercise 6.6 Question 9 (Page No. 438)
Use Algorithm $3$ to list all the $3$-combinations of $\{1, 2, 3, 4, 5\}.$

asked May 2 in Combinatory by Lakshman Patel RJIT | 8 views

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