Mukesh Kumar Nagar
@jiit.ac.in
Assistant Professor
Jaypee Institute of Information Technology Noida
EDUCATION
Ph.D, Postdoc
RESEARCH, TEACHING, or OTHER INTERESTS
Discrete Mathematics and Combinatorics, Algebra and Number Theory
Scopus Publications
Scholar Citations
Scholar h-index
Scopus Publications
Ali Azimi, Rakesh Jana, Mukesh Kumar Nagar, and Sivaramakrishnan Sivasubramanian
Elsevier BV
Mukesh Kumar Nagar, Arbind Kumar Lal, and Sivaramakrishnan Sivasubramanian
Informa UK Limited
Let T be a tree on n vertices and let be the q-analogue of its Laplacian. For a partition , let the normalized immanant of indexed by λ be denoted as . A string of inequalities among is known when λ varies over hook partitions of n as the size of the first part of λ decreases. In this work, we show a similar sequence of inequalities when λ varies over two row partitions of n as the size of the first part of λ decreases. Our main lemma is an identity involving binomial coefficients and irreducible character values of indexed by two row partitions. Our proof can be interpreted using the combinatorics of Riordan paths and our main lemma admits a nice probabilisitic interpretation involving peaks at odd heights in generalized Dyck paths or equivalently involving special descents in Standard Young Tableaux with two rows. As a corollary, we also get inequalities between and when and are comparable trees in the poset and when and are both two rowed partitions of n, with having a larger first part than .
Mukesh Kumar Nagar
Elsevier BV
Mukesh Kumar Nagar and Sivaramakrishnan Sivasubramanian
Elsevier BV
Mukesh Kumar Nagar and Sivaramakrishnan Sivasubramanian
Elsevier BV