论文标题
GGR猜想的新证明
A New Proof of the GGR Conjecture
论文作者
论文摘要
对于每个积极的整数$ n $，功能$ f $，以及点$ x $，Ghinchev，Guerragio的1998猜想和Rocca指出，存在$ n $ th $ n $ -th peano衍生物$ f _ {（n）}（x）$的存在与存在所有$ n（n+n+n+1）/2 $ 2 $ niviv riemant [ d_ {k，-j} f（x）= \ lim_ {h \ rightarrow 0} \ frac 1 {h^{k}} \ sum_ {i = 0}^k（-1）^k（-1）^i \ binom {k} n $。 $ n \ geq 2 $的版本用$ j $代替了所有$ -J $，并消除了所有$ j = k-1 $。作者最近使用基于高度非平凡的组合算法的非电感证明证明了GGR猜想及其版本。本文基于（laurent）多项式的减少，提供了这些定理中每个定理的简单，电感，代数证明。
For each positive integer $n$, function $f$, and point $x$, the 1998 conjecture by Ghinchev, Guerragio, and Rocca states that the existence of the $n$-th Peano derivative $f_{(n)}(x)$ is equivalent to the existence of all $n(n+1)/2$ generalized Riemann derivatives, \[ D_{k,-j}f(x)=\lim_{h\rightarrow 0}\frac 1{h^{k}}\sum_{i=0}^k(-1)^i\binom{k}{i}f(x+(k-i-j)h), \] for $j,k$ with $0\leq j<k\leq n$. A version of it for $n\geq 2$ replaces all $-j$ with $j$ and eliminates all $j=k-1$. Both the GGR conjecture and its version were recently proved by the authors using non-inductive proofs based on highly non-trivial combinatorial algorithms. This article provides a simple, inductive, algebraic proof of each of these theorems, based on a reduction to (Laurent) polynomials.
