arXiv subjects

Dipnit Biswas

Publications and source records attributed to Dipnit Biswas.

3 recordsLinked to original sources

arXiv2025

On the Polytope Model and Near End node Isomorphisms of Type $A$ Kirillov--Reshetikhin Crystals

We prove an inductive formula to construct a path from the highest weight element to any given vertex in the crystal graph of the polytope realization of the Kirillov-Reshetikhin crystal $KR^{i,m}$ of type $A$. For $i \leq 2$ or $i \geq n-1$, we provide explicit formulas of the same by only using the lowering crystal operators and in those cases, using these paths, we determine the explicit image of any element under the affine crystal isomorphisms between the polytope and the tableau realizations of the Kirillov-Reshetikhin crystals.

math.CO↗

arXiv2024

On the characterization of chordal graphs using Horn hypergeometric series

Radchenko and Villegas characterized the chordal graphs by the inverse of their independence polynomials being Horn hypergeometric series in Radchenko et al. in 2021. In this paper, we reprove their result using some elementary combinatorial methods. Our proof is different from their proof, and it is based on the connection between the inverse of the multi-variate independence polynomials and the multi-colored chromatic polynomials of graphs, established by Arunkumar et al. in 2018.

math.CO↗

arXiv2022

On symmetric closed subsets of real affine root systems

Any symmetric closed subset of a finite crystallographic root system must be a closed subroot system. This is not, in general, true for real affine root systems. In this paper, we determine when this is true and also give a very explicit description of symmetric closed subsets of real affine root systems. At the end, using our results, we study the correspondence between symmetric closed subsets of real affine root systems and the regular subalgebras generated by them.

math.RA↗