Related papers: Patterns in Shi tableaux and Dyck paths
We deduce decompositions of natural representations of general linear groups and symmetric groups from combinatorial bijections involving tableaux. These include some of Howe's dualities, Gelfand models, the Schur-Weyl decomposition of…
We investigate a natural Heyting algebra structure on the set of Dyck paths of the same length. We provide a geometrical description of the operations of pseudocomplement and relative pseudocomplement, as well as of regular elements. We…
An upward planar order on an acyclic directed graph $G$ is a special linear extension of the edge poset of $G$ that satisfies the nesting condition. This order was introduced to combinatorially characterize upward plane graphs and…
In queuing theory, it is usual to have some models with a "reset" of the queue. In terms of lattice paths, it is like having the possibility of jumping from any altitude to zero. These objects have the interesting feature that they do not…
This dissertation investigates the geometric combinatorics of convex polytopes and connections to the behavior of the simplex method for linear programming. We focus our attention on transportation polytopes, which are sets of all tables of…
Ascent sequences are sequences of nonnegative integers with restrictions on the size of each letter, depending on the number of ascents preceding it in the sequence. Ascent sequences have recently been related to (2+2)-free posets and…
In this paper we consider a few Calculus optimization problems in which we notice peculiar patterns. In each of these cases there is a geometric explanation for the pattern showing that it is not just a coincidence.
Matrix field theory is a combinatorially non-local field theory which has recently been found to be a non-trivial but solvable QFT example. To generalize such non-perturbative structures to other models, a more combinatorial understanding…
In this work, we introduce new combinatorial objects called Dyck tableaux, which present a natural insertion algorithm. These tools may be useful to describe statistics which are relevant in the study of the physical model named PASEP.
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…
Let A be a subspace arrangement and let chi(A,t) be the characteristic polynomial of its intersection lattice L(A). We show that if the subspaces in A are taken from L(B_n), where B_n is the type B Weyl arrangement, then chi(A,t) counts a…
We extend the the combinatorics of tableaux to the study of diagram algebras and give a uniform construction of their quasi-hereditary covers.
Keeping in mind the several models of M(atrix) theory we attempt to understand the possible structure of the topological M(atrix) theory ``underlying'' these approaches. In particular we are motivated by the issue about the nature of the…
It is shown that graphs that generalize the ADE Dynkin diagrams and have appeared in various contexts of two-dimensional field theory may be regarded in a natural way as encoding the geometry of a root system. After recalling what are the…
We revisit the behavioral approach to systems theory and make explicit the abstract pattern that governs it. Our end goal is to use that pattern to understand interaction-related phenomena that emerge when systems interact. Rather than…
We study natural one-parameter families of antiholomorphic correspondences arising from univalent restrictions of Shabat polynomials, indexed by rooted dessin d'enfants. We prove that the parameter spaces are topological quadrilaterals,…
Matrix models are a promising candidate for a nonperturbative formulation of the superstring theory. It is possible to study how the standard model and other phenomenological models appear from the matrix model, and estimate the probability…
The dual of a matrix ordered space has a natural matrix ordering that makes the dual space matrix ordered as well. The purpose of these notes is to give a condition that describes when the linear map taking a basis of the n by n matrices to…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
Recently O. Pechenik studied the cyclic sieving of increasing tableaux of shape $2\times n$, and obtained a polynomial on the major index of these tableaux, which is a $q$-analogue of refined small Schr\"{o}der numbers. We define…