A. Godbole

collaborators

3 papers

math.CO2026

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

VerÃ³nica BorrÃ¡s-Serrano, Isabel Byrne, Anant Godbole +1

Let $I ¨ _{n}$ 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.PR2026

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

Anant Godbole

The Erd\H os-RÃ©nyi 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 $\lo…

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…