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Singularity Analysis Via the Iterated Kernel Method
TLDR
In the quarter plane, five lattice path models with unit steps have resisted the otherwise general approach featured in recent works by Fayolle, Kurkova and Raschel. Expand
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On 3-Dimensional Lattice Walks Confined to the Positive Octant
Many recent papers deal with the enumeration of 2-dimensional walks with prescribed steps confined to the positive quadrant. The classification is now complete for walks with steps in $${\{0, \pmExpand
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Counting Partitions inside a Rectangle
TLDR
We consider the number of partitions of $n$ whose Young diagrams fit inside an $m \times \ell$ rectangle; equivalently, we study the coefficients of the $q$-binomial coefficient $\binom{m+\ell}{m}_q$. Expand
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Asymptotic Lattice Path Enumeration Using Diagonals
TLDR
We consider d-dimensional lattice path models restricted to the first orthant whose defining step sets exhibit reflective symmetry across every axis. Expand
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Analytic Combinatorics in Several Variables : Effective Asymptotics and Lattice Path Enumeration. (Combinatoire analytique en plusieurs variables : asymptotique efficace et énumération de chemin de
TLDR
The field of analytic combinatorics in several variables (ACSV) has shown how to deriveasymptotics for the coefficients of certain D-finite functions represented by diagonals ofmultivariate rational functions. Expand
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A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape
Tableau sequences of bounded height have been central to the analysis of k-noncrossing set partitions and matchings. We show here that familes of sequences that end with a row shape are particularlyExpand
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Higher Dimensional Lattice Walks: Connecting Combinatorial and Analytic Behavior
TLDR
We consider the enumeration of walks on the non-negative lattice $\mathbb{N}^d$, with steps defined by a set $\mathcal{S} \subset \{-1, 0, 1\}^D \setminus \{\mathbf{0}\}$. Expand
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Asymptotics of multivariate sequences in the presence of a lacuna
TLDR
We explain a discontinuous drop in the exponential growth rate for certain multivariate generating functions at a critical parameter value, in even dimensions $d \geq 4$. Expand
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Sequence Positivity Through Numeric Analytic Continuation: Uniqueness of the Canham Model for Biomembranes
TLDR
We prove solution uniqueness for the genus one Canham variational problem arising in the shape prediction of biomembranes. Expand
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