arXiv subjects

Rohun Easwar

Publications and source records attributed to Rohun Easwar.

3 recordsLinked to original sources

arXiv2026

Conditions for traceability under a bound on the size of even-distance sets

We make partial progress towards a proof of Conjecture 189 of Written on the Wall II by showing that a connected graph $G$ satisfying $\max\{\mathrm{dist_{even}}(v):v\in V(G)\}\le d_2+1$, where $\mathrm{dist_{even}}(v)$ is the number of vertices at an even distance from $v$ and $d_2$ is the second smallest degree of $G$, is traceable whenever at least one of four conditions holds. These conditions involve the vertex-connectivity, order, and diameter of $G$.

math.CO↗

arXiv2026

An application of Jacobi's residue formula and proofs of some other conjectures on binomial coefficients

We prove seven conjectures involving binomial coefficients. These conjectures appear in The On-Line Encyclopedia of Integer Sequences (OEIS). Among these is an application of Jacobi's residue formula. We also apply MacMahon's master theorem to give a new and independently obtained proof of a recently established result.

math.CO↗

arXiv2026

On Zeta functions and $μ$-series of string algebras

Let $\overlineμ_Λ(t):=\sum\limits_{m\geq1}μ_Λ(m)t^m$ be the \emph{$μ$-series} of a finite-dimensional tame algebra $Λ$ over an algebraically closed field, where $μ_Λ(m)$ denotes the minimal number of one-parameter families of $Λ$-modules with total dimension $m$. When $Λ$ is a string algebra with $\mathrm{Ba}(Λ)$ as its set of bands up to cyclic permutation, define the \emph{zeta function} $ζ_Λ(t):=\prod\limits_{\mathfrak b\in\mathrm{Ba}(Λ)}(1-t^{|\mathfrak b|})^{-1}$, where $|\mathfrak b|$ is the length of $\mathfrak b$. We prove an analogue of the prime number theorem for string algebras and use it to conclude that non-domestic string algebras are of exponential growth. Finally, we show that a string algebra is domestic if and only if its $μ$-series is rational.

math.RT↗