Related papers: A note on the Burrows-Wheeler transformation
We give an introduction to the theory of 2-Segal sets, and two of the main applications of them: Hall algebras and a discrete version of Waldhausen's $S_\bullet$-construction. We present several combinatorial examples and how these…
In this paper, we derive a formula on the integral of products of the higher-order Euler polynomials. By the same way, similar relations are obtained for $l$ higher-order Bernoulli polynomials and $r$ higher-order Euler polynomials.…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
An interesting phenomenon in combinatorics on words is when every recurrent word satisfying some avoidance constraints has the same factor set as a morphic word. An early example is the Hall-Thue word, fixed point of the morphism…
An introduction to Joyal's theory of combinatorial species is given and through it an alternative view of Rota's twelvefold way emerges.
Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…
We find some extensions of the Kraft-Russell Generic Equivalence Theorem and using it we obtain a simple proof of a result of Dubouloz and Kishimoto.
In this paper, we study Grothendieck polynomials from a combinatorial viewpoint. We introduce the factorial Grothendieck polynomials, analogues of the factorial Schur functions and present some of their properties, and use them to produce a…
When the co-recursion and co-dilation in the recurrence relation of certain sequences of orthogonal polynomials are not at the same level, the behaviour of the modified orthogonal polynomials is expected to have different properties…
The paper [GLZ] "L-functions of Carlitz modules, resultantal varieties and rooted binary trees" is devoted to a description of some resultantal varieties related to L-functions of Carlitz modules. It contains a conjecture that some of these…
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…
The Burrows-Wheeler Transform (BWT) of a string is an invertible permutation of the string, which can be used for data compression and compact indexes for string pattern matching. Ganguly et al. [SODA, 2017] introduced the parameterized BWT…
We present a short analytic proof of the equality between the analytic and combinatorial torsion. We use the same approach as in the proof given by Burghelea, Friedlander and Kappeler, but avoid using the difficult Mayer-Vietoris type…
In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We…
We give some results and conjectures about recurrence relations for certain sequences of binomial sums.
We highlight the correspondence between one-dimensional Lorentz transformations, which relate events observed from two distinct inertial reference frames, and ray transfer transformations in Gaussian optics. Specifically, we identify…
We show how to merge two run-length compressed Burrows-Wheeler Transforms (RLBWTs) into a run-length compressed extended Burrows-Wheeler Transform (eBWT) in $O (r)$ space and $O ((r + L) \log (m + n))$ time, where $m$ and $n$ are the…
In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory…
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
Article presents a short investigation into some properties of the Moser polynomials which appear in various problems from algebraic combinatorics. For instance, these polynomials can be used to solve the Generalized Moser's Problem on…