207 citations · 582 across the 40 of their papers we have counts for
42 papers
A central limit theorem for a generalization of the Ewens measure to random tuples of commuting permutations
Abdelmalek Abdesselam, Shannon Starr
We prove a central limit theorem (CLT) for the number of joint orbits of random tuples of commuting permutations. In the uniform sampling case this generalizes the classic CLT of G…
About the Hardy-Ramanujan partition function asymptotics
Shannon Starr
The Hardy-Ramanujan partition function asymptotics is a famous result in the asymptotics of combinatorial sequences. It was originally derived using complex analysis and number-the…
Violation of Ferromagnetic Ordering of Energy Levels in Spin Rings for the Singlet
David Heson, Shannon Starr, Jacob Thornton
We demonstrate a violation of the ``ferromagnetic ordering of energy levels'' conjecture (FOEL) for even length spin rings. The FOEL conjecture was a guess made by Nachtergaele, Sp…
Generating Function for Pinsky's Combinatorial Second Moment Formula for the Generalized Ulam Problem
Samen Hossein, Shannon Starr
Given a uniform random permutation , let be equal to the number of increasing subsequences of length : so $Z_{n,k}=|\{(i_1,\dots,i_k) \in \mathbb{Z}^k\, :\,…
Two Examples of COM Bounds using Spectral Gaps: Length of the LIS in a Random Permutation and Lipschitz Functions of 1d Markov Chains
Michael Froehlich, Shannon Starr
We consider two examples for a well-known method for obtaining concentration of measure (COM) bounds for a given observable in a given measure. The method is to consider an auxilia…
Rough Bounds for Emptiness Formation Probability in the 2d Dimer model using Reflection Positivity
Shannon Starr, Scott Williams
We summarize how to obtain rough bounds for one version of the emptiness formation probability in the 2d dimer model. The methods we use are the same as have been developed to obta…