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Recent questions tagged combinatory

4 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.
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 8 in Combinatory dd 362 views
0 votes
0 answers
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 $14.$ $3$ $89$ $111$
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 $n!$ ... respect to the correspondence between Cantor expansions and permutations as described in the preamble to question $14.$ $3$ $89$ $111$
asked May 1 in Combinatory Lakshman Patel RJIT 43 views
0 votes
0 answers
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 $14.$
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 $n!$ ... an algorithm for producing all permutations of a set of n elements based on the correspondence described in the preamble to question $14.$
asked May 1 in Combinatory Lakshman Patel RJIT 24 views
0 votes
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 $n!.$
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 1 in Combinatory Lakshman Patel RJIT 16 views
0 votes
0 answers
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. $246531$ $12345$ $654321$
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 $n!$ ... . Find the Cantor digits $a_{1}, a_{2},\dots,a_{n−1}$ that correspond to these permutations. $246531$ $12345$ $654321$
asked May 1 in Combinatory Lakshman Patel RJIT 21 views
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