# Mathematics Colloquium | Manjil Saikia

## November 23 @ 4:30 pm - 5:30 pm

- This event has passed.

### Event Details

__Speaker:__

**Manjil Saikia**

Postdoctoral Research Associate, School of Mathematics, Cardiff University

**Title:****Parity Biases in Partitions and Restricted Partitions**

**Meeting ID: 543 289 1076**

**Passcode: 8iaMX6**

**Recently, Kim, Kim & Lovejoy (2020) proved that partitions with more odd parts than even parts are more in number than partitions with more even parts than odd parts (for all n>2). This, they called as parity bias in integer partitions. We prove that this is true even if we restrict the partitions under consideration to that of distinct parts partitions (for all n>19). We also show that parity bias is reversed if we restrict the smallest part that can occur in a partition to 2 (for all n>7). Some other results of similar flavour can be proved for partitions where we restrict the set of allowed parts. All of these results are proved combinatorially. Using analytical techniques some of the inequalities can be further strengthened, we will discuss this as well as some related results for other classes of partitions, if time permits. This talk is based on joint work with K. Banerjee, S. Bhattacharjee, M. G. Dastidar & P. J. Mahanta as well as on a work in progress with P. J. Mahanta & A. Sarma.**

__Abstract:__

**About the Speaker**: Manjil Saikia is a Postdoctoral Research Associate in the School of Mathematics, Cardiff University working under Prof. Roger Behrend.

He completed his doctoral studies at the Faculty of Mathematics, the University of Vienna under the supervision of Prof. Ilse Fischer in September 2019. Prior to that, he did a Postgraduate Diploma from The Abdus Salam ICTP, Trieste (Italy) in 2015. During 2009 – 2014, he did his master’s in mathematics from Tezpur University, India.