论文标题
gapsets和$ k $的斐波那契序列
Gapsets and the $k$-generalized Fibonacci sequences
论文作者
论文摘要
在本文中，我们将数值半群的Kunz坐标的术语带入了差距，并将此概念推广到$ m $ extensions。它使我们能够识别带有板块倾斜的$ m $ extensions的差距。结果，我们证明了Bras-Amorós的一种版本，以$ M $ extensions进行猜想。此外，我们获得了具有固定属和深度的间隙数的下限，最多3个，以及一个上限的家族，用于具有固定属的间隙数。此外，当多重性为3或4时，我们为具有固定属和深度的差距的数量提供了明确的公式，在某些情况下，对于具有固定属和深度的差距的数量。
In this paper, 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 prove a version of Bras-Amorós conjecture for $m$-extensions. Besides, we obtain a lower bound for the number of gapsets with fixed genus and depth at most 3 and a family of upper bounds for the number of gapsets with fixed genus. 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.
