Recent questions tagged combinatory - GATE Overflow

+2 votes

1 answer

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 | 190 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 | 19 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 | 8 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 | 8 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 | 12 views

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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 | 7 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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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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11

Kenneth Rosen Edition 7th Exercise 6.6 Question 8 (Page No. 438)
Use Algorithm $2$ to list all the subsets of the set $\{1, 2, 3, 4\}.$

asked May 2 in Combinatory by Lakshman Patel RJIT | 6 views

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12

Kenneth Rosen Edition 7th Exercise 6.6 Question 7 (Page No. 438)
Use Algorithm $1$ to generate the $24$ permutations of the first four positive integers in lexicographic order.

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

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13

Kenneth Rosen Edition 7th Exercise 6.6 Question 6 (Page No. 438)
. Find the next larger permutation in lexicographic order after each of these permutations. $1342$ $45321$ $13245$ $612345$ $1623547$ f$23587416$

asked May 2 in Combinatory by Lakshman Patel RJIT | 11 views

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14

Kenneth Rosen Edition 7th Exercise 6.6 Question 5 (Page No. 438)
Find the next larger permutation in lexicographic order after each of these permutations. $1432$ $54123$ $12453$ $45231$ $6714235$ $31528764$

asked May 2 in Combinatory by Lakshman Patel RJIT | 14 views

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15

Kenneth Rosen Edition 7th Exercise 6.6 Question 4 (Page No. 438)
Suppose that the name of a file in a computer directory consists of three digits followed by two lowercase letters and each digit is $0, 1,\:\text{or}\: 2,$ and each letter is either $a\:\text{or}\: b.$ List the name of these files in lexicographic order, where we order letters using the usual alphabetic order of letters.

asked May 2 in Combinatory by Lakshman Patel RJIT | 11 views

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1 answer

16

Kenneth Rosen Edition 7th Exercise 6.6 Question 3 (Page No. 438)
The name of a file in a computer directory consists of three uppercase letters followed by a digit, where each letter is either $A, B,\:\text{ or}\: C,$ and each digit is either $1\: \text{or}\: 2.$ List the name of these files in lexicographic order, where we order letters using the usual alphabetic order of letters.

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

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1 answer

17

Kenneth Rosen Edition 7th Exercise 6.6 Question 2 (Page No. 438)
Place these permutations of $\{1,2,3,4,5,6\}$ in lexicographic order $:234561, 231456, 165432, 156423, 543216, 541236, 231465, 314562, 432561, 654321, 654312, 435612.$

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

0 votes

1 answer

18

Kenneth Rosen Edition 7th Exercise 6.6 Question 1 (Page No. 438)
Place these permutations of $\{1, 2, 3, 4, 5\}$ in lexicographic order $:43521, 15432, 45321, 23451, 23514, 14532, 21345, 45213, 31452, 31542.$

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

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1 answer

19

Kenneth Rosen Edition 7th Exercise 6.5 Question 66 (Page No. 434)
How many terms are there in the expansion of $(x + y + z)^{100}?$

asked May 1 in Combinatory by Lakshman Patel RJIT | 13 views

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