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Questions by Debashish Deka
User Debashish Deka
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User Debashish Deka
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+2
votes
0
answers
1
Graph Degree sequence : Bondy and Murty : $1.1.16$
asked
Jul 5
in
Graph Theory

116
views
graphtheory
nongate
proof
+1
vote
0
answers
2
Graph Theory : BondyMurty $1.1.20$
asked
Jul 5
in
Graph Theory

81
views
graphtheory
nongate
proof
+2
votes
0
answers
3
Graphic Sequence condition
A sequence $d = (d_1,d_2,\dots , d_n)$ is graphic if there is a simple graph with degree sequence $d$ If $d = (d_1,d_2,d_3, \dots d_n)$ is graphic and $d_1 \geq d_2 \geq d_3 \geq \dots \geq d_n$ , then show that $\sum_{i=1}^{n}d_i$ is even and $$\sum_ ... \leq \left [ k(k1) + \sum_{i=k+1}^{n} \min\{k,d_i\} \right ] \quad ,1 \leq k \leq n$$.
asked
Jul 4
in
Graph Theory

82
views
nongate
graphtheory
proof
+3
votes
0
answers
4
Minimum No. of vertices required
asked
Jul 1
in
Graph Theory

121
views
graphtheory
proof
+1
vote
0
answers
5
Equal coefficients
$\begin{align*} &A = \left ( p x + q \right )^{504} \text{ where p and q are +ve integers and }gcd(p,q) = 1 \\ &\text{Given } \left [ x^4 \right ] = \left [ x^5 \right ] , \text{ where } \left [ x^k \right ] \text{ denote the coefficient of }x^k \text{ in A.} \\ &\text{What is p+q ?} \end{align*}$
asked
Jul 1
in
Combinatory

26
views
discretemathematics
combinational
+3
votes
1
answer
6
Bitwise operation
#include <stdio.h> int main() { unsigned int m = 0; m = 0xA38; printf("%x\n",m(m1)); printf("%x\n",( (m(m1)) + 1 ) & m ); } Find the output ?
asked
Jun 28
in
Programming

55
views
programminginc
bitwise
+3
votes
1
answer
7
combinatorial argument
$\begin{align*} &\text{Prove using combinatorial argument } \\ &1) \qquad \text{For } n \geq k \geq 0 \qquad \left ( nk \right )\cdot \binom{n}{k} = n \cdot \binom{n1}{k} \\ &2) \qquad \text{For } n \geq 2 \qquad \quad k \cdot (k1) \cdot \binom{n}{k} = n \cdot (n1) \cdot \binom{n2}{k2} \\ \end{align*}$
asked
Jun 27
in
Combinatory

50
views
nongate
permutationsandcombinations
+1
vote
0
answers
8
Integer Sequence
$\begin{align*} &\text{A} = \text{Set of integer sequence }\left ( a_1,a_2,a_2 ,\dots , a_k \right ) \\ &\text{where } 1 \leq a_1 \leq a_2 \leq a_3 \leq \dots \leq a_k \leq n \\ &\text{B} = \text{Set of integer sequence }\left ( ... ; b_2 < b_3 < \dots < b_k \leq n \\ \end{align*}$ Prove that $\begin{align*} A = B \end{align*}$
asked
Jun 27
in
Combinatory

22
views
nongate
permutationsandcombinations
+1
vote
0
answers
9
Combinatoric properties
Prove that : $\begin{align*} &\text{For n , k , m are integers and } 0 < m \leq k < n \\ &\text{GCD}\left [ \binom{n}{m},\binom{n}{k} \right ] > 1 \\ \end{align*}$
asked
Jun 27
in
Combinatory

19
views
permutationsandcombinations
nongate
+3
votes
1
answer
10
Series Summation
Series summation of $S_n$ in closed form? $\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{align*}$
asked
Jun 11
in
Set Theory & Algebra

99
views
numbertheory
summation
discretemathematics
+1
vote
0
answers
11
Recursive fork()
The pid_t data type is a signed integer type which is capable of representing a process ID. getpid() returns the process ID of the current process The wait() system call suspends execution of the calling process until one of its children ... : some of the system call and macro definitions are simplified for the sake of the QS as well as for simplicity.
asked
Jun 2
in
Operating System

186
views
fork
operatingsystem
+1
vote
1
answer
12
Finding best time complexity
$\begin{align*} & a[n] = \{x_1,x_2,x_3,x_4,....,x_n\} \text{ is an array of integers where } n,x_i > 0. \\ & A = \left [ \text{min}\left ( x_i,x_j \right ) \right ] \cdot \left ( ji \right ) \text{ where } j ... } i,j \leq n \\ & \text{What is the best time complexity to find out the value of } A_{\bf max} \; ? \end{align*}$
asked
May 27
in
Algorithm Challenges

167
views
algorithms
timecomplexity
0
votes
1
answer
13
$a_n = 4^n + 6^n$
If $a_n = 4^n + 6^n$ Find the value of $a_{40} \text { mod } 25$
asked
May 19
in
Set Theory & Algebra

71
views
binomialdistribution
+1
vote
1
answer
14
2  connected graph
For a regular graph how much large the value of degree (for each vertices) should be such that the graph is $2$  connected. (vertex wise). I did in this way : $\begin{align*} &\quad \kappa(G) \leq \frac{2\cdot e}{n} \ ... regular and not 2 connected although $d \geq 2$ is satisfied. Why this $d \geq 2$ is trivial and not working in some cases ?
asked
May 19
in
Graph Theory

163
views
graphtheory
graphconnectivity
0
votes
1
answer
15
Placing rooks in nXn chess board
asked
May 4
in
Algorithms

115
views
nongate
recursion
game
permutationsandcombinations
+2
votes
1
answer
16
C programming  Output ?
Assume sizeof int as 4 #include <stdio.h> unsigned int L = (sizeof(unsigned int)) << 3; int foo(unsigned int m,unsigned int start,unsigned int length) { length = length >> 1; if(!length) { return m&(1<<start)?1:0; } ... length,length); return n1+n2; } } int main() { int m = 100; printf("%d\n",foo(m,0,L)); }
asked
Apr 29
in
Programming

316
views
programminginc
output
0
votes
1
answer
17
C programming
int main() { int n = 3,i,count=0; for(i=0;i<1<<n;i++) { int p = i; while(p) { int k = p & p; p = p  k; count++; } } } The value of count variable after execution of the above code? The value of count variable when $n = m$ ? [EDITED]
asked
Apr 20
in
Programming

94
views
programminginc
bitwise
+2
votes
4
answers
18
C programming  Output ?
#include <stdio.h> int main() { unsigned char a = 5; a = (1<<((sizeof(char)<<3)1)); char b = a; printf("%d %d\n",b,a); printf("%u %u\n",b,a); } If the size of a char datatype is 1 Byte, then what will be the output? [Edited]
asked
Apr 10
in
Programming

332
views
programminginc
+1
vote
2
answers
19
No of spanning Trees
Let $K_n$ denote the complete undirected graph with $n$ vertices where n is an even number. Find the maximum number of spanning trees of $K_n$ that can be formed in such a way that no two of these spanning trees have a common edge.
asked
Mar 19
in
Graph Theory

279
views
spanningtree
graphtheory
0
votes
0
answers
20
Recurrence relation and generating function
asked
Mar 19
in
Combinatory

114
views
generatingfunctions
permutationsandcombinations
recurrenceeqation
+1
vote
2
answers
21
c programming
#include <stdio.h> int K = 4; int a[2]; unsigned int m; int* check(unsigned int n) { int res = 1; int count = 0; for(int i=0;i<K;i++) if(!(n&(1<<i))) { count++; res = 0; } a[0] = res; a[1] = count; return a; } int foo( ... = x[1]; foo(mi,i+1); return count; } int main() { int x = foo(0,0); printf("%d\n",x); } value of x ___ ?
asked
Mar 19
in
Programming

162
views
programminginc
+1
vote
0
answers
22
Kenneth Rosen 6.444 advanced counting
asked
Mar 15
in
Combinatory

80
views
discretemathematics
generatingfunctions
recurrence
+1
vote
2
answers
23
Generating function
Let $h_n$ denote the number of nonnegative integral solutions of the equation $3x_1 + 4x_2 + 2x_3 + 5x_4 = n$ Find the generating function $g(x)$ for $h_0,h_1,h_2,h_3 ... h_n$
asked
Mar 15
in
Combinatory

108
views
generatingfunctions
permutationsandcombinations
+2
votes
1
answer
24
False sharing in cache Line
Here is pseudo code for a multiprocessing purpose: set_num_threads(NUM_THREADS); double sum=0.0; sum_local[NUM_THREADS]; parallel region { int this_thread_id = get_thread_number(); // returns 0 to (no_of_threads1) sum_local[this_thread_id] ... DRAM write back causing the problem, but not very clear, though. please explain a bit. @Arjun Sir
asked
Mar 6
in
CO & Architecture

126
views
co&architecture
cachememory
nongate
descriptive
0
votes
2
answers
25
Discrete math
The following is a sequence of formula, $$\begin{align*} \begin{matrix} & 9*1+2 &= &11 \\ & 9*12+3 &= &111 \\ & 9*123+4 &= &1111 \\ & 9*1234+5 &= &11111 \\ \end{matrix} \\ ... align*}$$ Here numbers are in base $10$. (a) Establish a formula in $\sum$ notation. (b) Generalize that formula in for any base $b$..
asked
Feb 26
in
Set Theory & Algebra

78
views
discretemathematics
descriptive
nongate
+2
votes
2
answers
26
Manipulation of sum
Prove the identity: $$\begin{align*} &\sum_{i=0}^{n}\sum_{j=0}^{i} a_ia_j = \frac{1}{2}\left ( \left ( \sum_{i=0}^{n}a_i \right )^2 + \left ( \sum_{i=0}^{n}a_i^2 \right )\right ) \end{align*}$$
asked
Feb 25
in
Combinatory

139
views
discretemathematics
summation
0
votes
2
answers
27
Discrete Math
Prove or disprove: $\begin{align*} \log_8x = \frac{1}{2}.\log_{2}x \end{align*}$.
asked
Feb 25
in
Set Theory & Algebra

98
views
discretemathematics
descriptive
nongate
0
votes
0
answers
28
Discrete math
Let $w \in \sum$$*$ be a string, with $\sum$ being the alphabet. Let $w^R$ be the reversal of string $w$, using induction prove that $(w^R)(w^R). . .(\text{for k times}) = (ww . . .(\text{for k times}))^R.$
asked
Feb 22
in
Set Theory & Algebra

56
views
descriptive
iitg_math
discretemathematics
0
votes
2
answers
29
Discrete Math
Prove or disprove the following: for finite sets A and B, $\overline{(A  B) \cup (B  A)} = A \cap B$ . If the proposition is incorrect, do minimal modifications to the same and prove.
asked
Feb 22
in
Set Theory & Algebra

91
views
discretemathematics
iitg_math
nongate
descriptive
0
votes
1
answer
30
Discrete math
Prove the following: $3 \;  \;\left ( a^2+b^2 \right )$ if and only if $3 \;  \;a$ and $3 \;  \;b$.
asked
Feb 22
in
Set Theory & Algebra

94
views
discretemathematics
iitg_math
descriptive
nongate
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