Related papers: Using alternating de Bruijn sequences to construct…
``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…
We introduce a new construction of towers of algebraic curves over finite fields and provide a simple example of an optimal tower.
We formulate and explain the extended Burrows-Wheeler transform of Mantaci et al from the viewpoint of permutations on a chain taken as a union of partial order-preserving mappings. In so doing we establish a link with syntactic semigroups…
Although it is well-known that the complex cobordism ring is a polynomial ring $\Omega_{*}^{U}\cong\mathbb{Z}\left[\alpha_{1},\alpha_{2},\ldots\right]$, an explicit description for convenient generators $\alpha_{1},\alpha_{2},\ldots$ has…
We count tilings of the $n \times m$ rectangular grid, cylinder, and torus with arbitrary tile sets up to arbitrary symmetries of the square and rectangle, along with cyclic shifting of rows and columns. This provides a unifying framework…
A construction that generates Williamson matrices of order $2n$ from Williamson matrices of odd order $n$ is presented. The construction is completely constructive and only uses three simple sequence operations.
We produce several algebraic curves, some well--known, some new, out of circles, by means of two classical (mutually reciprocal) algebraic methods: blow--down and blow--up.
We recall a construction of non-commutative algebras related to a one-parameter family of (deformed) spheres and tori, and show that in the case of tori, the *-algebras can be completed into C*-algebras isomorphic to the standard…
Try to generate new bridge types using generative artificial intelligence technology. Using symmetric structured image dataset of three-span beam bridge, arch bridge, cable-stayed bridge and suspension bridge , based on Python programming…
A new tool is introduced, specially tailored for the study of order 2 bases of N. It is called the Erdos-Tuan algebra since it suits well their conjecture.
Given one of an infinite class of supersymmetric quiver gauge theories, string theorists can associate a corresponding toric variety (which is a Calabi-Yau 3-fold) as well as an associated combinatorial model known as a brane tiling. In…
Tilting mutation is a way of producing new tilting complexes from old ones replacing only one indecomposable summand. In this paper, we give a purely combinatorial procedure for performing tilting mutation of suitable algebras. As an…
We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A_{2n}(2143) of alternating…
In this paper, we study a mirror duality on a generalized complex torus and a noncommutative complex torus. First, we derive a symplectic version of Riemann condition using mirror duality on ordinary complex tori. Based on this we will find…
Let k be a number field and K/k Galois. We transform the construction of the unramified Brauer group of the norm one torus R^1_K/k(G_m) into the construction of a special abelian extension over K. If k=Q and K/Q biquadratic, we explicitly…
The theme of this article is a "reciprocity" between bounded up-down paths and bounded alternating sequences. Roughly speaking, this ``reciprocity" manifests itself by the fact that the extension of the sequence of numbers of paths of…
Two subfamilies of Motzkin paths, with the same numbers of up, down, horizontal steps were known to be equinumerous with ternary trees and related objects. We construct a bijection between these two families that does not use any auxiliary…
We present new methods of generating Prouhet-Tarry-Escott partitions of arbitrarily large regularity. One of these methods generalizes the construction of the Thue-Morse sequence to finite alphabets with more than two letters. We show how…
The Clifford torus is a torus in a three-dimensional sphere. Homogeneous tori are simple generalization of the Clifford torus which still in a three-dimensional sphere. There is a way to construct tori in a three-dimensional sphere using…
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.