1 citations · 2 across the 14 of their papers we have counts for
17 papers
Distribution of the sum of reciprocal parts for distinct parts partitions
Walter Bridges
Given an integer partition of into distinct parts, the sum of the reciprocal parts is an example of an egyptian fraction. We study this statistic under the uniform measure on d…
Statistics for random representations of Lie algebras
Walter Bridges, Kathrin Bringmann, Caner Nazaroglu
In this paper we investigate how a typical, large-dimensional representation looks for a complex Lie algebra. In particular, we study the family o…
Zeros of Hook Polynomials and Related Questions
Walter Bridges, William Craig, Amanda Folsom +1
We study the zero set of polynomials built from partition statistics, complementing earlier work in this direction by Boyer, Goh, Parry, and others. In particular, addressing a que…
On the Proportion of Coprime Fractions in Number Fields
Walter Bridges, Johann Franke, Johann Christian Stumpenhusen
In this paper we determine the asymptotic density of coprime fractions in those of the reduced fractions of number fields. When ordered by norms of denominators, we count a fractio…
On the number of irreducible representations of
Walter Bridges, Kathrin Bringmann, Johann Franke
In this note, we use a variant of the hyperbola method to prove an asymptotic expansion for the summatory function of the number of irreducible -representations o…
On the distribution of the norm of partitions
Walter Bridges, William Craig
The norm of an integer partition is defined as the product of its parts. This statistic was recently introduced by Schneider in connection to partition zeta functions. In this note…
Log-concavity for unimodal sequences
Walter Bridges, Kathrin Bringmann
In this paper, we prove that the number of unimodal sequences of size is log-concave. These are coefficients of a mixed false modular form and have a Rademacher-type exact form…
A Rademacher-type exact formula for partitions without sequences
Walter Bridges, Kathrin Bringmann
In this paper we prove an exact formula for the number of partitions without sequences. By work of Andrews, the corresponding generating function is a product of a modular form and…
Asymptotic expansions for partitions generated by infinite products
Walter Bridges, Benjamin Brindle, Kathrin Bringmann +1
Recently, Debruyne and Tenenbaum proved asymptotic formulas for the number of partitions with parts in () and good analytic prop…
Taylor coefficients of false Jacobi forms and ranks of unimodal sequences
Walter Bridges, Kathrin Bringmann
We apply the new framework for modularity of false theta functions developed by the second author and Nazaroglu to study the asymptotic behavior of Taylor coefficients of false Jac…
Sign changes in statistics for plane partitions
Walter Bridges, Johann Franke, Joshua Males
Recent work of Cesana, Craig and the third author shows that the trace of plane partitions is asymptotically equidistributed in residue classes mod . Applying a technique of the…
Weighted cylindric partitions
Walter Bridges, Ali Uncu
Recently Corteel and Welsh outlined a technique for finding new sum-product identities by using functional relations between generating functions for cylindric partitions and a the…
Asymptotics for the twisted eta-product and applications to sign changes in partitions
Walter Bridges, Johann Franke, Taylor Garnowski
We prove asymptotic formulas for the complex coefficients of , where is a root of unity, and apply our results to determine secondary terms in the asymptoti…
Statistics for Unimodal Sequences
Walter Bridges, Kathrin Bringmann
We prove a number of limiting distributions for statistics for unimodal sequences of positive integers by adapting a probabilistic framework for integer partitions introduced by Fr…
Partitions into distinct parts with bounded largest part
Walter Bridges
We prove an asymptotic formula for the number of partitions of into distinct parts where the largest part is at most for fixed . Our method follow…
Limit Shapes for Unimodal Sequences
Walter Bridges
We prove asymptotic 0-1 Laws satisfied by diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane, and the upper boundary is…
Partition Inequalities and Applications to Sum-Product Conjectures of Kanade-Russell
Walter Bridges
We consider differences of one- and two-variable finite products and provide combinatorial proofs of the nonnegativity of certain coefficients. Since the products may be interprete…