Related papers: A Continuous Analogue for Young Diagrams
Unexpected product formulas for the number of standard Young tableaux of certain truncated shapes are found and proved. These include shifted staircase shapes minus a square in the NE corner, rectangular shapes minus a square in the NE…
We present a bijection between the set of standard Young tableaux of staircase minus rectangle shape, and the set of marked shifted standard Young tableaux of a certain shifted shape. Numerically, this result is due to DeWitt (2012).…
We present a survey on analog models of computations. Analog can be understood both as computing by analogy, or as working on the continuum. We consider both approaches, often intertwined, with a point of view mostly oriented by computation…
Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains…
We consider a graph called a lattice diagram, which is a graph in the $xy$-plane such that each edge is parallel to the $x$-axis or the $y$-axis. In [4], we investigated transformations of certain lattice diagrams, and we considered the…
We define a new partial order on $SYT_n$, the set of all standard Young tableaux with $n$ cells, by combining the chain order with the notion of horizontal strips. We prove various desirable properties of this new order.
We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an…
The Young--Fibonacci graph is the Hasse diagram of one of the two (along with the Young lattice) 1-differential graded modular lattices. This explains the interest to path enumeration problems in this graph. We obtain a formula for the…
We study the regime of anticipated synchronization recently described on a number of dynamical systems including chaotic and noisy ones. We use simple linear caricatures to show the minimal setups able to reproduce the basic facts…
We describe recent advances in the study of random analogues of combinatorial theorems.
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
In the paper I considered definition and structure of linear mapping of Banach algebra over commutative ring. Based on this definition I explore derivative of continuous mapping.
We propose to consider ensembles of cycles (quadrics), which are interconnected through conformal-invariant geometric relations (e.g. "to be orthogonal", "to be tangent", etc.), as new objects in an extended Moebius--Lie geometry. It was…
As an extension of positive or almost positive diagrams and links, we introduce a notion of successively almost positive diagrams and links, and good successively almost positive diagrams and links. We review various properties of positive…
We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive. This provides a universal method for…
We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…
Principles of analogical reasoning have recently been applied in the context of machine learning, for example to develop new methods for classification and preference learning. In this paper, we argue that, while analogical reasoning is…
The set of permutations on a finite set can be given a lattice structure (known as the weak Bruhat order). The lattice structure is generalized to the set of words on a fixed alphabet $\Sigma = \{ x, y, z, ... \}$, where each letter has a…
Cylindric Young tableaux are combinatorial objects that first appeared in the 1990s. A natural extension of the classical notion of a Young tableau, they have since been used several times, most notably by Gessel and Krattenthaler and by…
A modified version of the Dijkstra algorithm using an inventive contraction hierarchy is proposed. The algorithm considers a directed acyclic graph with a conical or semi-circular structure for which a pair of edges is chosen iteratively…