Related papers: Inserting rim-hooks into reverse plane partitions

Spin Hamiltonian engineering in solid-state systems plays a key role in a variety of applications ranging from quantum information processing and quantum simulations to novel studies of many-body physics. By analyzing the irreducible form…

Herein, we study an inverse problem for detecting unknown obstacles by the enclosure method using the Dirichlet--to--Neumann map for measurements. We justify the method for an penetrable obstacle case involving a biharmonic equation. We use…

A method is described for constructing, with computer assistance, planar substitution tilings that have n-fold rotational symmetry. This method uses as prototiles the set of rhombs with angles that are integer multiples of pi/n, and…

We use a regular arrangement of kirigami elements to demonstrate an inverse design paradigm for folding a flat surface into complex target configurations. We first present a scheme using arrays of disclination defect pairs on the dual to…

This habilitation thesis summarizes the research that I have carried out from 2005 to 2019. It is organized in four chapters. The first three deal with random planar maps. Chapter 1 is about their metric properties: from a general…

We exactly evaluate the partition function (index) of N=4 supersymmetric quiver quantum mechanics in the Higgs phase by using the localization techniques. We show that the path integral is localized at the fixed points, which are obtained…

We introduce the problem of partitioning 2D regions (usually convex regions) into mutually congruent pieces ('tiles').

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective…

In this article, we study hook lengths of ordinary partitions and $t$-regular partitions. We establish hook length biases for the ordinary partitions and motivated by them we find a few interesting hook length biases in $2$-regular…

Patience Sorting is a combinatorial algorithm that can be viewed as an iterated, non-recursive form of the Schensted Insertion Algorithm. In recent work the authors extended Patience Sorting to a full bijection between the symmetric group…

We investigate the $K$-theoretic Gysin map for type $A$ partial flag bundles from the viewpoint of integrability. We introduce several types of partition functions for one version of $q=0$ degeneration of $U_q(\widehat{sl_n})$ vertex models…

Bressoud introduced the partition function $B(\alpha_1,\ldots,\alpha_\lambda;\eta,k,r;n)$, which counts the number of partitions with certain difference conditions. Bressoud posed a conjecture on the generating function for the partition…

We show that the reformulation of the geometric Robinson-Schensted-Knuth (gRSK) correspondence via local moves, introduced in \cite{OSZ14} can be extended to cases where the input matrix is replaced by more general polygonal,…

A jet algorithm must specify how to (re-)combine different partons or towers into a single four-vector. Various recombination schemes have been used experimentally to examine the transverse energy profile of jets in hadron colliders.…

We present a computational and statistical approach for fitting isotonic models under convex differentiable loss functions. We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such…

We study computational aspects of repulsive Gibbs point processes, which are probabilistic models of interacting particles in a finite-volume region of space. We introduce an approach for reducing a Gibbs point process to the hard-core…

We construct an equivariant coarse homology theory arising from the algebraic $K$-theory of spherical group rings and use this theory to derive split injectivity results for associated assembly maps. On the way, we prove that the…

In this paper, we prove a result on the bisection of mass assignments by parallel hyperplanes on Euclidean vector bundles. Our methods consist of the development of a novel lifting method to define the configuration space--test map scheme,…

Back in the nineties Pak and Stanley introduced a labeling of the regions of a k-Shi arrangement by k-parking functions and proved its bijectivity. Duval, Klivans, and Martin considered a modification of this construction associated with a…

This paper contains a partial answer to the open problem 3.11 of \cite{[H2008]}. That is to find an explicit bijection on Schr\"oder paths that inverts the statistics area and bounce. This paper started as an attempt to write the sum over…