+91-674-249-4082

Submitted by klpatra on 4 April, 2017 - 09:56

Date/Time:

Thursday, April 13, 2017 - 15:30 to 16:30

Venue:

M4

Speaker:

Prof. S. Krishnan

Affiliation:

IIT Bombay

Title:

Hook Immanantal and Hadamard inequalities for q-Laplacians of trees

$\textbf{Abstract:}$ Let $T$ be a tree on $n$ vertices with Laplacian matrix $L$ and $q$-Laplacian $\mathcal{ L}_q$.
Let $\chi_k$ be the character of the irreducible representation of $\mathfrak{S}_n$ indexed by
the hook partition $k,1^{n-k}$ and let $\overline{ d}_k(L)$ be the normalized hook immanant of
$L$ corresponding to the character $\chi_k$. Inequalities for $\overline{ d}_k(L)$ as $k$ increases are known.
By assigning a statistic to vertex orientations on trees, we generalize these
inequalities to the $q$-analogue $\mathcal{ L}_q$ of $L$ for all $q \in \mathbb{R}$ and to the
bivariate $q,t$-Laplacian $\mathcal{ L}_{q,t}$ for some values $q,t$.
Our statistic based approach also generalizes several
other inequalities including the changing index $k(L)$ of the
Hadamard inequality for $L$, to the matrix $\mathcal{ L}_q$ and $\mathcal{ L}_{q,t}$. Thus, we
extend several results about $L$ to $\mathcal{ L}_q$ which includes the case when $\mathcal{ L}_q$
is not positive semidefinite.

**School of Mathematical Sciences**

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

Corporate Site - This is a contributing Drupal Theme

Design by WeebPal.

Design by WeebPal.