This is a collection of some revision notes. They include topics discussed in first three sessions of Combinatorics Course at Cheenta (Faculty: Ashani Dasgupta).

combinatorics 1(work sheet)

- Study of
**symmetry**in geometry is greatly facilitated by combinatorial methods- There are 6 symmetries of an equilateral triangle (=3! permutations of 3 things)
- There are 8 symmetries of a square (8 out of 4! permutations of 4 things are used up)
- All 24 symmetries (including orientations) of a tetrahedron account for 4! permutations of 4 things

**Cycle notation**helps in exploiting permutations- Length of a cycle equals it’s order

**Bijection Principle**helps to count sets which are otherwise difficult to count.- Number of non negative integer solutions of a + b + c + d = n is \(\displaystyle{ \binom{n+3}{3}} \)
- We use balls and bars technique to do this

**Partitions**- Conjugate Partitions and Ferrar’s diagram
- Catalan Numbers