Mubin Shaikh

Variance of random greedy independent sets in triangle-free graphs

This preprint studies the size of the independent set produced by processing the vertices of a fixed finite graph in uniformly random order, accepting each vertex when none of its neighbors has previously been accepted. For every finite simple triangle-free graph G with n ≥ 2 ver...

Variance of random greedy independent sets in triangle-free graphs

This preprint studies the size of the independent set produced by processing the vertices of a fixed finite graph in uniformly random order, accepting each vertex when none of its neighbors has previously been accepted. For every finite simple triangle-free graph G with n ≥ 2 ver...

Rationality and Quasipolynomiality of Restricted Rectangle Partitions

This preprint presents a proof of Conjecture 5.10 of Gajdzica, Visser, and Zakarczemny on restricted rectangle partitions.For every fixed positive integer k, let f_k(n) count multisets of bars of sizes 1 × j, with 1 ≤ j ≤ k, that can tile a 2 × n rectangle. Rotations are allowed,...