Mukesh Kumar Nagar

@jiit.ac.in

Assistant Professor
Jaypee Institute of Information Technology Noida

Mukesh Kumar Nagar


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https://researchid.co/mukesh.kr.nagar

EDUCATION

Ph.D, Postdoc

RESEARCH, TEACHING, or OTHER INTERESTS

Discrete Mathematics and Combinatorics, Algebra and Number Theory
7

Scopus Publications

24

Scholar Citations

2

Scholar h-index

1

Scholar i10-index

Scopus Publications

  • The maximum four point condition matrix of a tree
    Ali Azimi, Rakesh Jana, Mukesh Kumar Nagar, Sivaramakrishnan Sivasubramanian
    Linear Algebra and Its Applications, 2024
  • Four-point condition matrices of edge-weighted trees
    Ali Azimi, Rakesh Jana, Mukesh K. Nagar, Sivaramakrishnan Sivasubramanian
    Special Matrices, 2024
    Formulas for the determinant of distance matrix D T {D}_{T} of tree T T are known in the unweighted case and in the case when the edges of T T have commuting variable weights. Associated with the four-point condition (4PC) and a tree T T are two matrices, the Max4PC T {{\\rm{Max4PC}}}_{T} and the Min4PC T {{\\rm{Min4PC}}}_{T} . These are not full rank matrices and their rank, a basis B B , and formulas for the determinant when restricted to the rows and columns of B B are known. In this work, we generalize both these matrices to the case when the edges of T T have commuting variable weights and determine edge-weighted counterparts of known results.
  • Inequalities among two rowed immanants of the q-Laplacian of trees and odd height peaks in generalized Dyck paths
    Mukesh Kumar Nagar, Arbind Kumar Lal, Sivaramakrishnan Sivasubramanian
    Journal of Difference Equations and Applications, 2022
    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 .
  • Eigenvalue monotonicity of q-Laplacians of trees along a poset
    Mukesh Kumar Nagar
    Linear Algebra and Its Applications, 2019
  • Laplacian immanantal polynomials and the GTS poset on trees
    Mukesh Kumar Nagar, Sivaramakrishnan Sivasubramanian
    Linear Algebra and Its Applications, 2019
  • GENERALIZED MATRIX POLYNOMIALS OF TREE LAPLACIANS INDEXED BY SYMMETRIC FUNCTIONS AND THE GTS POSET
    Seminaire Lotharingien De Combinatoire, 2019
  • Hook immanantal and Hadamard inequalities for q-Laplacians of trees
    Mukesh Kumar Nagar, Sivaramakrishnan Sivasubramanian
    Linear Algebra and Its Applications, 2017

RECENT SCHOLAR PUBLICATIONS

  • Four-point condition matrices of edge-weighted trees
    A Azimi, R Jana, MK Nagar, S Sivasubramanian
    Special Matrices 12 (1), 20240011 , 2024
    2024
  • The maximum four point condition matrix of a tree
    A Azimi, R Jana, MK Nagar, S Sivasubramanian
    Linear Algebra and its Applications 691, 133-150 , 2024
    2024
    Citations: 2
  • On the Min4PC matrix of a tree
    A Azimi, R Jana, M Nagar, S Sivasubramanian
    American Journal of Combinatorics 3, 13–21-13–21 , 2024
    2024
    Citations: 1
  • Laplacian Immanantal Polynomials of a Bipartite Graph and Graph Shift Operation
    MK Nagar
    arXiv preprint arXiv:2307.15979 , 2023
    2023
  • Inequalities among two rowed immanants of the q -Laplacian of trees and odd height peaks in generalized Dyck paths
    MK Nagar, AK Lal, S Sivasubramanian
    Journal of Difference Equations and Applications 28 (2), 198-221 , 2022
    2022
  • Generalized Matrix polynomials of Tree Laplacians indexed by Symmetric functions and the GTS poset
    MK Nagar, S Sivasubramanian
    arXiv preprint arXiv:1912.03101 , 2019
    2019
    Citations: 2
  • Eigenvalue monotonicity of q-Laplacians of trees along a poset
    MK Nagar
    Linear Algebra and its Applications 571, 110-131 , 2019
    2019
    Citations: 2
  • Laplacian immanantal polynomials and the GTS poset on trees
    MK Nagar, S Sivasubramanian
    Linear Algebra and its Applications 561, 1-23 , 2019
    2019
    Citations: 6
  • Hook immanantal and Hadamard inequalities for q-Laplacians of trees
    MK Nagar, S Sivasubramanian
    Linear Algebra and its Applications 523, 131-151 , 2017
    2017
    Citations: 11
  • A q and q; t-analogue of Hook Immanantal Inequalities and Hadamard Inequality for Trees
    MK Nagar, S Sivasubramanian
    2016

MOST CITED SCHOLAR PUBLICATIONS

  • Hook immanantal and Hadamard inequalities for q-Laplacians of trees
    MK Nagar, S Sivasubramanian
    Linear Algebra and its Applications 523, 131-151 , 2017
    2017
    Citations: 11
  • Laplacian immanantal polynomials and the GTS poset on trees
    MK Nagar, S Sivasubramanian
    Linear Algebra and its Applications 561, 1-23 , 2019
    2019
    Citations: 6
  • The maximum four point condition matrix of a tree
    A Azimi, R Jana, MK Nagar, S Sivasubramanian
    Linear Algebra and its Applications 691, 133-150 , 2024
    2024
    Citations: 2
  • Generalized Matrix polynomials of Tree Laplacians indexed by Symmetric functions and the GTS poset
    MK Nagar, S Sivasubramanian
    arXiv preprint arXiv:1912.03101 , 2019
    2019
    Citations: 2
  • Eigenvalue monotonicity of q-Laplacians of trees along a poset
    MK Nagar
    Linear Algebra and its Applications 571, 110-131 , 2019
    2019
    Citations: 2
  • On the Min4PC matrix of a tree
    A Azimi, R Jana, M Nagar, S Sivasubramanian
    American Journal of Combinatorics 3, 13–21-13–21 , 2024
    2024
    Citations: 1
  • Four-point condition matrices of edge-weighted trees
    A Azimi, R Jana, MK Nagar, S Sivasubramanian
    Special Matrices 12 (1), 20240011 , 2024
    2024
  • Laplacian Immanantal Polynomials of a Bipartite Graph and Graph Shift Operation
    MK Nagar
    arXiv preprint arXiv:2307.15979 , 2023
    2023
  • Inequalities among two rowed immanants of the q -Laplacian of trees and odd height peaks in generalized Dyck paths
    MK Nagar, AK Lal, S Sivasubramanian
    Journal of Difference Equations and Applications 28 (2), 198-221 , 2022
    2022
  • A q and q; t-analogue of Hook Immanantal Inequalities and Hadamard Inequality for Trees
    MK Nagar, S Sivasubramanian
    2016