Related papers: Christoffel Matrices and Sturmian Determinants

The aim of this paper is to study determinants of matrices related to the Pascal triangle.

Borel and Reutenauer (2006) showed, \emph{inter alia}, that a word $w$ of length $n>1$ is conjugate to a Christoffel word if and only if for $k=0,1, \dots , n-1$, $w$ has $k+1$ distinct circular factors of length $k$. Sturmian words are the…

Performing both right and left multiplication operations using general regular matrix polynomials, which need not be monic and may possess leading coefficients of arbitrary rank, on a rectangular matrix of measures associated with mixed…

A Redheffer--type matrix with Fibonacci entries is defined, and the determinant and spectral properties of this matrix are studied. Also, more general Redheffer--type matrices are considered and intriguing number-theoretic examples are…

We extend the classical Ostrowski numeration systems, closely related to Sturmian words, by allowing a wider range of coefficients, so that possible representations of a number $n$ better reflect the structure of the associated Sturmian…

This paper is dedicated to compute Pfaffian and determinant of one type of skew centrosymmetric matrices in terms of general number sequence of second order.

We give a new combinatorial explanation for well-known relations between determinants and traces of matrix powers. Such relations can be used to obtain polynomial-time and poly-logarithmic space algorithms for the determinant. Our new…

Using recurrence matrices, defined and described with some details, we study a few determinants related to evaluations of binomial coefficients on Dirichlet characters modulo 2, 4 and 8.

We compute the motive of the classifying stack of an orthogonal group in the Grothendieck ring of stacks over a field of characteristic different from two.

We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by…

We define a family of natural decompositions of Sturmian words in Christoffel words, called *reversible Christoffel* (RC) factorizations. They arise from the observation that two Sturmian words with the same language have (almost always)…

Motivated by the theory of trapezoidal words, whose sequences of cardinality of factors by length are symmetric, we introduce a bivariate variant of this symmetry. We show that this symmetry characterizes Christoffel words, and establish…

This article presents methods to efficiently compute the Coriolis matrix and underlying Christoffel symbols (of the first kind) for tree-structure rigid-body systems. The algorithms can be executed purely numerically, without requiring…

We introduce a new geometric approach to Sturmian words by means of a mapping that associates certain lines in the n x n -grid and sets of finite Sturmian words of length n. Using this mapping, we give new proofs of the formulas enumerating…

A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.

We use the Jacobi-Trudi formula to execute "explicit" evaluation of determinants of Stirling numbers of both kinds. We also offer a Maple package accompanying the paper on the personal websites at the end of the second page.

The purpose of this article is to extend the earliest results of A.A. Brudno, connecting topological entropy of a subshift X over $\mathbb{N}$ to the Kolmogorov complexity of words in X, to subshifts over computable groups that posses…

We show that the first-order theory of Sturmian words over Presburger arithmetic is decidable. Using a general adder recognizing addition in Ostrowski numeration systems by Baranwal, Schaeffer and Shallit, we prove that the first-order…

This paper investigates the Stirling numbers of the first and second kind associated with a delta series f (t). These numbers provide a robust framework that satisfies the orthogonality and inverse relations, often lacking in recent…

We give a combinatorial interpretation of the determinant of a matrix as a generating function over Brauer diagrams in two different but related ways. The sign of a permutation associated to its number of inversions in the Leibniz formula…