Related papers: A combinatorial model for the transition matrix be…
In this paper, we study the staircase encoding of permutations, which maps a permutation to a staircase grid with cells filled with permutations. We consider many cases, where restricted to a permutation class, the staircase encoding…
Traversals are commonly seen in tree data structures, and performance-enhancing transformations between tree traversals are critical for many applications. Existing approaches to reasoning about tree traversals and their transformations are…
We study the crossing matrix of a braid and introduce a polynomial invariant for braid systems that is invariant under Hurwitz equivalence. As an application to the study of surface braids and surface links, we also define an invariant that…
Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang--Baxter equation, and the isotropic state with an adjustable parameter is found to…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
A grid class consists of permutations whose pictorial depiction can be partitioned into increasing and decreasing parts as determined by a given matrix. In this paper, we introduce a method for enumerating cyclic permutations in vector grid…
In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here…
We study the combinatorial and structural properties of the circle map sequences. We introduce an embedding procedure which gives a map from the hull(closure of the set of translates) to the sequence of embedding operations through which we…
We describe a new method for combinatorially computing the transverse invariant in knot Floer homology. Previous work of the authors and Stone used braid diagrams to combinatorially compute knot Floer homology of braid closures. However,…
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope \pm1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods,…
By extending the notion of grid classes to include infinite grids, we establish a structural characterisation of the simple permutations in Av(4231, 35142, 42513, 351624), a pattern class which has three different connections with algebraic…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
We introduce an evolutionary metacommunity of multitrophic food webs on several habitats coupled by migration. In contrast to previous studies that focus either on evolutionary or on spatial aspects, we include both and investigate the…
We report the discovery of a discrete hierarchy of micro-transitions occurring in models of continuous and discontinuous percolation. The precursory micro-transitions allow us to target almost deterministically the location of the…
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected…
The study of pinnacle sets has been a recent area of interest in combinatorics. Given a permutation, its pinnacle set is the set of all values larger than the values on either side of it. Largely inspired by conjectures posed by Davis,…
In the modeling, monitoring, and control of complex networks, a fundamental problem concerns the comprehensive determination of the state of the system from limited measurements. Using power grids as example networks, we show that this…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
This set of Montreal lectures is an elementary and sketchy introduction to the general field of random matrices. The first half is devoted to combinatorial models, whereas the second half deals with random matrix questions(GUE, etc...).
Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…