Example .1 Find an exponential generating function for the number of permutations with repetition of length nn of…

We have talked about the number of ways to properly color a graph with kk colors, given…

Binomial theorem, statement that for any positive integer n, the nth power of the sum of two numbers a and b may…

Pascal's identity, first derived by Blaise Pascal in 17th century, states that the number of ways…

A permutation is an arrangement of some elements in which order matters. In other words a Permutation…

Spanning tree of a graph is a subgraph of it which forms a tree and contains…

From the First Principle of Counting we have arrived at the commutativity of addition, which was expressed in convenient…

A rooted tree is a tree with a special vertex labelled as the "root" the of tree.…

Chromatic number of a graph is the minimum value of kk for which the graph is k-colorablek-colorable. In other…

Not all graphs are planar. If there are too many edges and too few vertices,…