Chris Jennings-Shaffer

activity

20132024

most citedExotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and Bailey Pairs From Groups A, C, E

16 citations · 34 across the 16 of their papers we have counts for

collaborators

30 papers

q-bio.PE2024★ 3 cited

Finding high posterior density phylogenies by systematically extending a directed acyclic graph

Chris Jennings-Shaffer, David H Rich, Matthew Macaulay +7

Bayesian phylogenetics typically estimates a posterior distribution, or aspects thereof, using Markov chain Monte Carlo methods. These methods integrate over tree space by applying…

math.NT2021

Graph Schemes, Graph Series, and Modularity

Kathrin Bringmann, Chris Jennings-Shaffer, Antun Milas

To a simple graph we associate a so-called graph series, which can be viewed as the Hilbert--Poincaré series of a certain infinite jet scheme. We study new $q$ -representations and…

math.NT2020★ 7 cited

Further $q$ -series identities and conjectures relating false theta functions and characters

Chris Jennings-Shaffer, Antun Milas

In this short note, a companion of [20], we discuss several families of $q$ -series identities in connection to false and mock theta functions, characters of modules of vertex algeb…

math.NT2020

On $q$ -series identities for false theta series

Chris Jennings-Shaffer, Antun Milas

We prove several infinite families of $q$ -series identities for false theta functions and related series. These identities are motivated by considerations of characters of modules…

math.NT2019

The Asymptotic Distribution of the Rank for Unimodal Sequences

Kathrin Bringmann, Chris Jennings-Shaffer, Karl Mahlburg

We study the asymptotic behavior of the rank statistic for unimodal sequences. We use analytic techniques involving asymptotic expansions in order to prove asymptotic formulas for…

math.NT2019

On a Tauberian Theorem of Ingham and Euler-Maclaurin Summation

Kathrin Bringmann, Chris Jennings-Shaffer, Karl Mahlburg

We discuss two theorems in analytic number theory and combinatory analysis that have seen increased use in recent years. A corollary to a Tauberian theorem of Ingham allows one to…

math.NT2019

Some $q$ -series identities extending work of Andrews, Crippa, and Simon on sums of divisors functions

Kathrin Bringmann, Chris Jennings-Shaffer

In this article we extend a theorem of Andrews, Crippa, and Simon on the asymptotic behavior of polynomials defined by a general class of recursive equations. Here the polynomials…

math.NT2018

Unimodal Sequence Generating Functions Arising from Partition Ranks

Kathrin Bringmann, Chris Jennings-Shaffer

In this paper we study generating functions resembling the rank of strongly unimodal sequences. We give combinatorial interpretations, identities in terms of mock modular forms, as…

math.NT2018

Proofs and reductions of various conjectured partition identities of Kanade and Russell

Kathrin Bringmann, Chris Jennings-Shaffer, Karl Mahlburg

We prove seven of the Rogers-Ramanujan type identities modulo $12$ that were conjectured by Kanade and Russell. Included among these seven are the two original modulo $12$ identiti…

math.NT2018

Peak positions of strongly unimodal sequences

Kathrin Bringmann, Chris Jennings-Shaffer, Karl Mahlburg +1

We study combinatorial and asymptotic properties of the rank of strongly unimodal sequences. We find a generating function for the rank enumeration function, and give a new combina…

math.NT2018

Asymptotic Formulas Related to the $M_{2}$ -rank of Partitions without Repeated Odd Parts

Chris Jennings-Shaffer, Dillon Reihill

We give asymptotic expansions for the moments of the $M_{2}$ -rank generating function and for the $M_{2}$ -rank generating function at roots of unity. For this we apply the Hardy-Ramanu…

math.NT2018

A note on Andrews' partitions with parts separated by parity

Kathrin Bringmann, Chris Jennings-Shaffer

In this note we give three identities for partitions with parts separated by parity, which were recently introduced by Andrews.

math.PR2017

When Fourth Moments Are Enough

Chris Jennings-Shaffer, Dane R. Skinner, Edward C. Waymire

This note concerns a somewhat innocent question motivated by an observation concerning the use of Chebyshev bounds on sample estimates of $p$ in the binomial distribution with para…

math.NT2017

Mock modularity of the $M_{d}$ -rank of overpartitions

Chris Jennings-Shaffer, Holly Swisher

We investigate the modular properties of a new partition rank, the $M_{d}$ -rank of overpartitions. In fact this is an infinite family of ranks, indexed by the positive integer $d$ , t…

math.NT2016

On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramanujan's $ω (q)$

Kathrin Bringmann, Chris Jennings-Shaffer, Karl Mahlburg

We analyze the mock modular behavior of $P ˉ_{ω} (q)$ , a partition function introduced by Andrews, Dixit, Schultz, and Yee. This function arose in a study of smallest parts functi…

math.NT2016

Higher Order Smallest Parts Functions and Rank-Crank Moment Inequalities from Bailey Pairs

Catherine Babecki, Chris Jennings-Shaffer, Geoffrey Sangston

We generalize a result of Garvan on inequalities and interpretations of the moments of the partition rank and crank functions. In particular for nearly 30 Bailey pairs, we introduc…

math.NT2016

Overpartition Rank Differences Modulo 7 By Maass Forms

Chris Jennings-Shaffer

Using that the overpartition rank function is the holomorphic part of a harmonic Maass form, we deduce formulas for the rank differences modulo 7. To do so we make improvements on…

math.NT2016

The generating function of the $M_{2}$ -rank of partitions without repeated odd parts as a mock modular form

Chris Jennings-Shaffer

By work of Bringmann, Ono, and Rhoades it is known that the generating function of the $M_{2}$ -rank of partitions without repeated odd parts is the so-called holomorphic part of a ce…

math.NT2015

Ranks For Two Partition Quadruple Functions

Chris Jennings-Shaffer

Recently the author introduced two new integer partition quadruple functions, which satisfy Ramanujan-type congruences modulo $3$ , $5$ , $7$ , and $13$ . Here we reprove the congruenc…

math.NT2015

Some Smallest Parts Functions from Variations of Bailey's Lemma

Chris Jennings-Shaffer

We construct new smallest parts partition functions and smallest parts crank functions by considering variations of Bailey's Lemma and conjugate Bailey pairs. The functions we intr…

math.NT2015

Two partition functions with congruences modulo 3, 5, 7, and 13

Chris Jennings-Shaffer

We introduce two new integer partition functions, both of which are the number of partition quadruples of $n$ with certain size restrictions. We prove both functions satisfy Ramanu…

math.NT2015

Exotic Bailey-Slater SPT-Functions III: Bailey Pairs from Groups B, F, G, and J

Chris Jennings-Shaffer

We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simp…

math.NT2015★ 16 cited

Exotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and Bailey Pairs From Groups A, C, E

Frank Garvan, Chris Jennings-Shaffer

We investigate spt-crank-type functions arising from Bailey pairs. We recall four spt-type functions corresponding to the Bailey pairs $A 1$ , $A 3$ , $A 5$ , and $A 7$ of Slater and give…

math.NT2014

Exotic Bailey-Slater SPT-Functions I: Group A

Chris Jennings-Shaffer

We introduce several spt-type functions that arise from Bailey pairs. We prove simple Ramanujan type congruences for these functions which can be explained by a spt-crank-type func…

Finding high posterior density phylogenies by systematically extending a directed acyclic graph

Graph Schemes, Graph Series, and Modularity

Further q-series identities and conjectures relating false theta functions and characters

On q-series identities for false theta series

The Asymptotic Distribution of the Rank for Unimodal Sequences

On a Tauberian Theorem of Ingham and Euler-Maclaurin Summation

Some q-series identities extending work of Andrews, Crippa, and Simon on sums of divisors functions

Unimodal Sequence Generating Functions Arising from Partition Ranks

Proofs and reductions of various conjectured partition identities of Kanade and Russell

Peak positions of strongly unimodal sequences

Asymptotic Formulas Related to the M2​-rank of Partitions without Repeated Odd Parts

A note on Andrews' partitions with parts separated by parity

When Fourth Moments Are Enough

Mock modularity of the Md​-rank of overpartitions

On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramanujan's ω(q)

Higher Order Smallest Parts Functions and Rank-Crank Moment Inequalities from Bailey Pairs

Overpartition Rank Differences Modulo 7 By Maass Forms

The generating function of the M2​-rank of partitions without repeated odd parts as a mock modular form

Ranks For Two Partition Quadruple Functions

Some Smallest Parts Functions from Variations of Bailey's Lemma

Two partition functions with congruences modulo 3, 5, 7, and 13

Exotic Bailey-Slater SPT-Functions III: Bailey Pairs from Groups B, F, G, and J

Exotic Bailey-Slater SPT-Functions II: Hecke-Rogers-Type Double Sums and Bailey Pairs From Groups A, C, E

Exotic Bailey-Slater SPT-Functions I: Group A

Further $q$ -series identities and conjectures relating false theta functions and characters

On $q$ -series identities for false theta series

Some $q$ -series identities extending work of Andrews, Crippa, and Simon on sums of divisors functions

Asymptotic Formulas Related to the $M_{2}$ -rank of Partitions without Repeated Odd Parts

Mock modularity of the $M_{d}$ -rank of overpartitions

On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramanujan's $ω (q)$

The generating function of the $M_{2}$ -rank of partitions without repeated odd parts as a mock modular form