Related papers: Insertion algorithms for Gelfand $S_n$-graphs
Kirchhoff's matrix-tree theorem states that the number of spanning trees of a graph G is equal to the value of the determinant of the reduced Laplacian of $G$. We outline an efficient bijective proof of this theorem, by studying a canonical…
The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
Fomin (1994) introduced a notion of duality between two graded graphs on the same set of vertices. He also introduced a generalization to dual graded graphs of the classical Robinson-Schensted-Knuth algorithm. We show how Fomin's approach…
Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…
We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…
A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018)…
We show how, given a sufficiently large point cloud sampled from an embedded 2-manifold in $\mathbb{R}^n$, we may obtain a global representation as a cell complex with vertices given by a representative subset of the point cloud. The vertex…
Let $S$ be a semigroup, $\Lambda$ a non-empty set and $P$ a mapping of $\Lambda$ into $S$. The set $S\times \Lambda$ together with the operation $\circ _P$ defined by $(s, \lambda)\circ _P(t, \mu )=(sP(\lambda)t, \mu )$ form a semigroup…
We describe a combinatorial approach for investigating properties of rational numbers. The overall approach rests on structural bijections between rational numbers and familiar combinatorial objects, namely rooted trees. We emphasize that…
This paper establishes an analogue of the Robinson--Schensted correspondence for cylindric tableaux. In particular, for any pair of positive integers $(d,L)$, we construct a bijection between permutations that avoid the patterns $d\cdots 1…
The paper is devoted to the study of some well-knonw combinatorial functions on the symmetric group $\sn$ --- the major index $\maj$, the descent number $\des$, and the inversion number $\inv$ --- from the representation-theoretic point of…
Bauer and Itzykson showed that associated to each labeled map embedded on an oriented Riemann surface there was a group generated by a pair of permutations. From this result an algorithm may be constructed for enumerating labeled maps, and…
The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…
We prove that insertion-elimination Lie algebra of Feynman graphs, in the ladder case, has a natural interpretation in terms of a certain algebra of infinite dimensional matrices. We study some aspects of its representation theory and we…
This article presents a unified bijective scheme between planar maps and blossoming trees, where a blossoming tree is defined as a spanning tree of the map decorated with some dangling half-edges that enable to reconstruct its faces. Our…
We extend Schaeffer's bijection between rooted quadrangulations and well-labeled trees to the general case of Eulerian planar maps with prescribed face valences, to obtain a bijection with a new class of labeled trees, which we call…
A conjecture by Deutsch, Kitaev, and Remmel states that the triples of permutation statistics $(S_{10}, S_{12}, S_{17})$ and $(S_{12}, S_{10} ,S_{17})$ are equidistributed over the symmetric group $\mathfrak{S}_n$. Here, $S_{10}$ enumerates…
We show that the theory of sorting by reversals fits into the well-established theory of circuit partitions of 4-regular multigraphs (which also involves the combinatorial structures of circle graphs and delta-matroids). In this way, we…
The inclusion of symmetries as an inductive bias, known as equivariance, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for…
We carry out the complete group classification of the class of (1+1)-dimensional linear Schr\"odinger equations with complex-valued potentials. After introducing the notion of uniformly semi-normalized classes of differential equations, we…