Related papers: Growth diagrams, Domino insertion and Sign-imbalan…
We analyse the so-called Marginal Instability of linear switching systems, both in continuous and discrete time. This is a phenomenon of unboundedness of trajectories when the Lyapunov exponent is zero. We disprove two recent conjectures of…
We describe two constructions of (very) dense graphs which are edge disjoint unions of large {\em induced} matchings. The first construction exhibits graphs on $N$ vertices with ${N \choose 2}-o(N^2)$ edges, which can be decomposed into…
Based on empirical evidence obtained using the {\sf CHEVIE} computer algebra system, we present a series of conjectures concerning the combinatorial description of the Kazhdan--Lusztig cells for type $B_n$ with unequal parameters. These…
We present a general technique for addressing sign problems that arise in Monte Carlo simulations of field theories. This method deforms the domain of the path integral to a manifold in complex field space that maximizes the average sign…
Generalizing the kink operator of the Heisenberg spin 1/2 model, we construct a set of Klein factors explicitly such that $(1+1)$ dimensional fermion theories with arbitrary number of species are mapped onto the corresponding boson theories…
We study the seeded domino problem, the recurring domino problem and the $k$-SAT problem on finitely generated groups. These problems are generalization of their original versions on $\mathbb{Z}^2$ that were shown to be undecidable using…
We present Monte Carlo calculations of the thermodynamics of the (2+1) dimensional Thirring model at finite density. We bypass the sign problem by deforming the domain of integration of the path integral into complex space in such a way as…
Using the Berele/Remmel/Kerov/Vershik variation of the Robinson-Schensted-Knuth correspondence, we study the cycle and increasing subsequence structure after various methods of shuffling. One consequence is a cycle index for shuffles like:…
We consider $m$ integral vectors $X_1,...,X_m \in \mathbb{Z}^s$ located in a half-space of $\mathbb{R}^s$ ($m\ge s\geq 1$) and study the structure of the additive semi-group $X_1 \mathbb{N} +... + X_m \mathbb{N}$. We introduce and study…
We show that corner polyhedra and 3-connected Schnyder labelings join the growing list of planar structures that can be set in exact correspondence with (weighted) models of quadrant walks via a bijection due to Kenyon, Miller, Sheffield…
We extend a previous conjecture [cond-mat/0407477] relating the Perron-Frobenius eigenvector of the monodromy matrix of the O(1) loop model to refined numbers of alternating sign matrices. By considering the O(1) loop model on a…
The antiferromagnetic Heisenberg chain is expected to have an extended symmetry, [SU(2)xSU(2)]/Z 2 , in the infrared limit, whose physical interpretation is that the spin and dimer order parameters form the components of a common…
Dinur, Khot, Kindler, Minzer and Safra (2016) recently showed that the (imperfect completeness variant of) Khot's 2 to 2 games conjecture follows from a combinatorial hypothesis about the soundness of a certain "Grassmanian agreement…
We perform a detailed analysis of the fermionic sign problem in a series of one dimensional integrals, that are achieved as extreme (one-site) limits of genuine physics models. Altogether we studied a Hubbard-like, a Gross-Neveu-like, a…
In this paper, we firstly extend a result of Bonin, Shapiro and Simion by giving the distribution of the major index over generalized Schr\"{o}der paths. Then by providing a bijection between generalized Schr\"{o}der paths and…
In the semisimple case, we derive (asymptotic) formulas for the growth rate of the number of summands in tensor powers of the generating object in diagram/interpolation categories.
We examine domino tilings of rectangular boards, which are in natural bijection with perfect matchings of grid graphs. This leads to the study of their associated perfect matching polytopes, and we present some of their properties, in…
In the first part of this lecture, the 1/N expansion technique is illustrated for the case of the large-N sigma model. In large-N gauge theories, the 1/N expansion is tantamount to sorting the Feynman diagrams according to their degree of…
We study a special case of the configuration model, in which almost all the vertices of the graph have degree $2$. We show that the graph has a very peculiar and interesting behaviour, in particular when the graph is made up by a vast…
We show how the sign of a permutation can be deduced from the tableaux induced by the permutation under the Robinson-Schensted-Knuth correspondence. The result yields a simple proof of a conjecture on the squares of imbalances raised by…