Related papers: Robinson-Schensted Algorithms Obtained from Tablea…
Motivated by Stanley's results in \cite{St02}, we generalize the rank of a partition $\lambda$ to the rank of a shifted partition $S(\lambda)$. We show that the number of bars required in a minimal bar tableau of $S(\lambda)$ is max$(o, e +…
A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…
Our results can be viewed as applications of algebraic combinatorics in random matrix theory. These applications are motivated by the predictive power of random matrix theory for the statistical behavior of the celebrated Riemann…
We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan…
Set-valued tableaux, introduced by Buch to express the tableaux-sum formula for stable Grothendieck polynomials, generalize semistandard tableaux. We provide a new recursive proof that the number of set-valued tableaux of a given shape is…
Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of…
This article is part of an ongoing investigation of the two-dimensional Jacobian conjecture. In the first paper of this series, we proved the generalized Magnus' formula. In this paper, inspired by cluster algebras, we introduce a sequence…
Through the following, we establish the conditions which allow us to express recursive sequences of real numbers, enumerated through the recurrence relation a_{n+1} = Aa_n + Ba_{n-1}, by means of algebraic equations in two variables of…
In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single…
We introduce an insertion algorithm on Kohnert's combinatorial model for Demazure characters, generalizing Robinson--Schensted--Knuth insertion on tableaux. Our new insertion yields an explicit, nonnegative formula expressing the product of…
Robinsonian matrices arise in the classical seriation problem and play an important role in many applications where unsorted similarity (or dissimilarity) information must be reordered. We present a new polynomial time algorithm to…
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…
Given a matrix $D$ describing the pairwise dissimilarities of a data set, a common task is to embed the data points into Euclidean space. The classical multidimensional scaling (cMDS) algorithm is a widespread method to do this. However,…
We define a class of computable functions over real numbers using functional schemes similar to the class of primitive and partial recursive functions defined by G\"odel and Kleene. We show that this class of functions can also be…
We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by…
A fundamental identity in the representation theory of the partition algebra is $n^k = \sum_{\lambda} f^\lambda m_k^\lambda$ for $n \geq 2k$, where $\lambda$ ranges over integer partitions of $n$, $f^\lambda$ is the number of standard Young…
In [2], while studying a relevant class of polyominoes that tile the plane by translation, i.e., double square polyominoes, the authors found that their boundary words, encoded by the Freeman chain coding on a four letters alphabet, have…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…