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Combinatorics | Number Theory
Find the transitive closure of the relation using Warshall’s algorithm R={(1,2),(2,1),(2,3),(3,4),(4,1)} on the set {1,2,3,4}.
Combinatorics | Number Theory
Is the `divides’ relation on the set of positive integers
(a) reflexive? (b) symmetric? (c) transitive? (d) an equivalence relation?
Justify your answers.
(a) reflexive? (b) symmetric? (c) transitive? (d) an equivalence relation?
Justify your answers.
Combinatorics | Number Theory
For the poset ({2,4,6,9,12,18,27,36,48,60,72},|) having the `divides’ relation, find
(a) the maximal elements
(b) the minimal elements
(c) All upper bounds of {2,9}
(d) The least upper bound of {2,9} if it exists.
(a) the maximal elements
(b) the minimal elements
(c) All upper bounds of {2,9}
(d) The least upper bound of {2,9} if it exists.
Combinatorics | Number Theory
What is a partially ordered set? Prove that the inclusion relation `is a subset of’ is a partial ordering on the power set of a finite set S.
Combinatorics | Number Theory
Use generating functions to solve the recurrence relation a_k=5a_(k-1)-6a_(k-2) with the initial conditions a_0=6 and a_1=30.
Combinatorics | Number Theory
Use generating functions to solve the recurrence relation a_k=3a_(k-1)+4^(k-1) with the initial condition a_0=1.
Combinatorics | Number Theory
Find the solution of the recurrence relation a_n=4a_(n-1)-4a_(n-2)+(n+1).2^n.
Combinatorics | Number Theory
Find the solution of the recurrence relation a_n=2a_(n-1)+〖3.2〗^n.
Combinatorics | Number Theory
Find all solutions of the recurrence relation a_n=5a_(n-1)-6a_(n-2)+2^n+3n.
Combinatorics | Number Theory
Find the general form of the solutions of the recurrence relation a_n=8a_(n-2)-16a_(n-4).
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