论文标题
WILF猜想向半模块的扩展在数值半群上
An extension of the Wilf conjecture to semimodules over a numerical semigroup
论文作者
论文摘要
本文的目的是通过一种新的方法向数字半群上的数字半群上的半模块扩展到半模块，以在数值半群上求解Wilf猜想的解决方案。关键点是引入一个新的不变式，我们称之为半群的Wilf功能，该功能也可以定义为在半群上的半模块。我们还研究了半群的WILF函数的关系以及与半群缝隙相关的某些半模块的WILF功能。结果，我们获得了一个替代猜想，这也意味着Wilf猜想。最后，我们表明，除非我们使用了半模块的WILF函数，否则WILF猜想对半模型的自然概括不起作用。在这个方向上，我们提出了几个问题，内容涉及半模块的WILF型不平等的可能扩展。
The aim of this paper is to propose an extension of the Wilf conjecture to semimodules over a numerical semigroup through a new approach toward the solution of the Wilf conjecture on numerical semigroups. The key point is the introduction of a new invariant that we call Wilf function of a semigroup that can be also defined for a semimodule over the semigroup. We also study the relation of the Wilf function of a semigroup and the Wilf function of certain semimodules associated to a gap of the semigroup. As a consequence, we obtain an alternative conjecture which also implies the Wilf conjecture. Finally, we show that the natural generalization of Wilf conjecture to semimodules over the semigroup does not work unless we used the Wilf function of the semimodule. In this direction, we propose several questions regarding the possible extensions of Wilf-type inequalities for semimodules.
