A. Godbole

activity

20052026

most citedSierpi\' nski Gasket Graphs and Some of Their Properties

19 citations · 93 across the 45 of their papers we have counts for

collaborators

52 papers

math.PR2026

The Expected Number of Distinct Substrings in an Alphabet String

Anant Godbole

Consider a sequence of i.i.d.~trials $X = {X_{1}, X_{2}, \dots, X_{n}}$ where $p (X_{i} = j) = 1 / d; j = 1, 2, \dots, d$ , or more generally $p (X_{i} = j) = p_{j}; \sum_{1 \leq j \leq d} p_{j} = 1$ . We consider…

math.PR2026

An Erd\H os Rényi Law for the Longest Consecutive Monotone Block in a Random Permutation

Anant Godbole

The Erd\H os-Rényi law states that given a sequence ${X_{j}}_{j = 1}^{\infty}$ of i.i.d.~( $p$ ) coin-tosses, the longest run $L_{n}$ of heads in the first $n$ coin tosses approaches $\log…

math.CO2026

A Lower Bound on the Expected Number of Distinct Patterns in a Random Permutation

Verónica Borrás-Serrano, Isabel Byrne, Anant Godbole +1

Let $π_{n}$ be a uniformly chosen random permutation on $[n]$ . The authors of [2] showed that the expected number of distinct consecutive patterns of all lengths $k\in\{1,2,\ldots,n\…

math.CO2025

A Resolution of the McCarty Conjecture

Anant Godbole, Lybitina Koene, Grant Shirley

The McCarty Conjecture states that any McCarty Matrix (an $n \times n$ matrix $A$ with positive integer entries and each of the $2 n$ row and column sums equal to $n$ ), can be additi…

math.CO2023

No-Three-in-a- $Θ :$ Variations on the No-Three-in-a-Line Problem

Natalie Dodson, Anant Godbole, Dashleen Gonzalez +2

We pose a natural generalization to the well-studied and difficult no-three-in-a-line problem: How many points can be chosen on an $n \times n$ grid such that no three of them form…

math.CO2023

An Alternative Proof for the Expected Number of Distinct Consecutive Patterns in a Random Permutation

Anant Godbole, Hannah Swickheimer

Let $π_{n}$ be a uniformly chosen random permutation on $[n]$ . Using an analysis of the probability that two overlapping consecutive $k$ -permutations are order isomorphic, the author…