Related papers: Experimenting with Standard Young Tableaux
We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
Explainability in yield prediction helps us fully explore the potential of machine learning models that are already able to achieve high accuracy for a variety of yield prediction scenarios. The data included for the prediction of yields…
We introduce a simple extension of the $\lambda$-calculus with pairs---called the distributive $\lambda$-calculus---obtained by adding a computational interpretation of the valid distributivity isomorphism $A \Rightarrow (B\wedge C)\ \…
Let SYT_n be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYT_n and some of their crucial properties, we prove three main results:…
One way to investigate the precision of estimates likely to result from planned experiments and planned epidemiological studies is to simulate a large number of possible outcomes and analyse the sets of possible results. This appears to be…
Cayley's formula states that the number of labelled trees on $n$ vertices is $n^{n-2}$, and many of the current proofs involve complex structures or rigorous computation. We present a bijective proof of the formula by providing an…
Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed…
Computational simulations are a popular method for testing hypotheses about the emergence of communication. This kind of research is performed in a variety of traditions including language evolution, developmental psychology, cognitive…
Symbolic computation, powered by modern computer algebra systems, has important applications in mathematical reasoning through exact deep computations. The efficiency of symbolic computation is largely constrained by such deep computations…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
Dyck paths are one of the most important objects in enumerative combinatorics, and there are many papers devoted to counting selected families of Dyck paths. Here we present two approaches for the automatic counting of many such families,…
Exact evaluation of $<{\rm Tr} S^p>$ is here performed for real symmetric matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix entries are independent identically distributed random variables, with an arbitrary…
Barely set-valued tableaux are a variant of Young tableaux in which one box contains two numbers as its entry. It has recently been discovered that there are product formulas enumerating certain classes of barely set-valued tableaux. We…
Query answering routinely employs knowledge graphs to assist the user in the search process. Given a knowledge graph that represents entities and relationships among them, one aims at complementing the search with intuitive but effective…
In this work we suggest the use of a set-theoretical interpretation of semantic tableaux for teaching propositional logic. If the student has previous notions of basic set theory, this approach to semantical tableaux can clarify her the way…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…
We use Experimental Mathematics and Symbolic Computation (with Maple), to search for lots and lots of Perrin- and Lucas- style primality tests, and try to sort the wheat from the chaff. More impressively, we find quite a few such primality…
The possibility of interaction between Maple and numeric compiled languages in performing extensive numeric calculations is exemplified by the Ndynamics package, a tool for studying the (chaotic) behavior of dynamical systems. Programming…
Tables are an extremely powerful visual and interactive tool for structuring and manipulating data, making spreadsheet programs one of the most popular computer applications. In this paper we introduce and address the task of recommending…