论文标题
多元差异Gončarov多项式
Multivariate Difference Gončarov Polynomials
论文作者
论文摘要
当数值分析中的经典Gončarov插值问题通过用Delta运算符替换衍生物时，单变量DeltaGončarov多项式会出现。当所考虑的三角洲运算符是向后差的运算符时，我们将获得单变量差异gončarov多项式，该多项式与给定的右边界具有与平面的晶格路径具有组合关系。在本文中，我们将单变量差异的几种代数和分析特性扩展到多元案例。然后，我们根据$ d $ TUB的某些限制来建立多元差异多项式的组合解释。这激发了多元差异Gončarov多项式与高维广义停车功能之间的联系，即$ \ boldsymbol {u} $ - 停车功能，我们从中根据多元多变的DeltaGončarovpolynomials从中得出了几个枚举结果。
Univariate delta Gončarov polynomials arise when the classical Gončarov interpolation problem in numerical analysis is modified by replacing derivatives with delta operators. When the delta operator under consideration is the backward difference operator, we acquire the univariate difference Gončarov polynomials, which have a combinatorial relation to lattice paths in the plane with a given right boundary. In this paper, we extend several algebraic and analytic properties of univariate difference Gončarov polynomials to the multivariate case. We then establish a combinatorial interpretation of multivariate difference Gončarov polynomials in terms of certain constraints on $d$-tuples of non-decreasing integer sequences. This motivates a connection between multivariate difference Gončarov polynomials and a higher-dimensional generalized parking function, the $\boldsymbol{U}$-parking function, from which we derive several enumerative results based on the theory of multivariate delta Gončarov polynomials.
