Related papers: Robinson-Schensted Algorithms Obtained from Tablea…
Given a permutation $\sigma$, the Robinson-Schensted correspondence determines a certain partition called the shape of $\sigma$. Famously, the shape measures the longest unions of increasing and decreasing subsequences, thus giving global…
Bosons and fermions are often written by elements of other algebras. M. Abe gave a recursive realization of the boson by formal infinite sums of the canonical generators of the Cuntz algebra ${\cal O}_{\infty}$. We show that such formal…
Combinatorial transition matrices arise frequently in the theory of symmetric functions and their generalizations. The entries of such matrices often count signed, weighted combinatorial structures such as semistandard tableaux, rim-hook…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
We introduce and initiate the study of a new model of reductions called the random noise model. In this model, the truth table $T_f$ of the function $f$ is corrupted on a randomly chosen $\delta$-fraction of instances. A randomized…
We derive computable formulas for the structured backward errors of a complex number $\lambda$ when considered as an approximate eigenvalue of rational matrix polynomials that carry a symmetry structure. We consider symmetric,…
After a short introduction on Clifford algebras of polynomials, we give a general method of constructing a matrix representation. This process of linearization leads naturally to two fundamental structures: the generalized Clifford algebra…
We show that several families of polynomials defined via fillings of diagrams satisfy linear recurrences under a natural operation on the shape of the diagram. We focus on key polynomials, (also known as Demazure characters), and Demazure…
Reynolds' theory of relational parametricity formalizes parametric polymorphism for System F, thus capturing the idea that polymorphically typed System F programs always map related inputs to related results. This paper shows that Reynolds'…
We consider linear mappings on the $d$-dimensional torus, defined by $T(x) = Ax \pmod 1$, where $A$ is an invertible $d \times d$ integer matrix, with no eigenvalues on the unit circle. In the case $d = 2$ and $\det A = \pm 1$, we give a…
A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension $d$ is proposed. The relation between $d$ and $d-2$ dimensional integrals is given in terms of a…
The Fibonacci number is the residue of a rational function, from which follows that Fibonacci number summation identities can be derived with the integral representation method, a method also used to derive combinatorial identities. A…
Many machine learning applications deal with high dimensional data. To make computations feasible and learning more efficient, it is often desirable to reduce the dimensionality of the input variables by finding linear combinations of the…
Geometric number systems, obtained by extending the real number system to include new anticommuting square roots of +1 and -1, provide a royal road to higher mathematics by largely sidestepping the tedious languages of tensor analysis and…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…
We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infinite context, obtaining matrices that are not necessarily…
In this article we investigate how we can employ the structure of combinatorial objects like Hadamard matrices and weighing matrices to device new quantum algorithms. We show how the properties of a weighing matrix can be used to construct…
Let $\lambda=(\lambda_1 \geqslant \ldots \geqslant \lambda_k > 0)$. For any $c$ Coxeter element of $\mathfrak{S}_{\lambda_1+k-1}$, we construct a bijection from fillings of $\lambda$ to reverse plane partitions. We recover two previous…
We approach Riordan arrays and their generalizations via umbral symbolic methods. This new approach allows us to derive fundamental aspects of the theory of Riordan arrays as immediate consequences of the umbral version of the classical…
If $x$ is a non-empty string then the repetition $xx$ is called a tandem repeat. Similarly, a tandem in a two dimensional array $X$ is a configuration consisting of a same primitive block $W$ that touch each other with one side or corner.…