Hall 123

Eliminating linear relations in combinatorial enumerations

Kamalakshya Mahatab

IMSc

Many combinatorial problems can be thought of as counting certain types of n-tuples, or more generally, classes of n-tuples. For example, number of partitions of three can be represented by 3-tuples (e.g. (2, 1, 0) ) whose coordinates sum to 3. But not all such tuples we will count; as there are some repetitions(e.g. (2, 1, 0) and (1, 2, 0) represent the same partition). The problems, where these repetitions can be represented by linear relations, will be analyzed in this talk. We will use some results on Grobner basis for our purpose. We will go through these concepts with some examples.