Gapsets and the k-generalized Fibonacci sequences

IF 0.5 2区数学 Q3 MATHEMATICS

International Journal of Algebra and Computation Pub Date : 2024-04-03 DOI:10.1142/s0218196724500085

Gilberto B. Almeida Filho, Matheus Bernardini

引用次数: 0

Abstract

We bring the terminology of the Kunz coordinates of numerical semigroups to gapsets and we generalize this concept to m-extensions. It allows us to identify gapsets and, in general, m-extensions with tilings of boards; as a consequence, we present some applications of this identification. Moreover, we present explicit formulas for the number of gapsets with fixed genus and depth, when the multiplicity is 3 or 4, and, in some cases, for the number of gapsets with fixed genus and depth.

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缺口集和 k 个广义斐波那契序列

我们将数字半群的 Kunz 坐标术语引入间隙集，并将这一概念推广到 m-扩展。这样，我们就能识别间隙集，一般来说，也能识别 m-扩展与棋盘的倾斜；因此，我们介绍了这种识别的一些应用。此外，当多重性为 3 或 4 时，我们给出了具有固定属和深度的隙集数的明确公式，并在某些情况下给出了具有固定属和深度的隙集数的明确公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Algebra and Computation 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.