اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدProof of the $(alpha,beta)$--inversion formula conjectured by Hsu and Ma
127
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In light of the well-known fact that the $n$th divided difference of any polynomial of degree $m$ must be zero while $m<n$,the present paper proves the $(alpha,beta)$-inversion formula conjectured by Hsu and Ma [J. Math. Res. $&$ Exposition 25(4) (2005) 624]. As applications of $(alpha,beta)$-inversion, we not only recover some known matrix
قيم البحث
اقرأ أيضاً
In this note, using the derangement polynomials and their umbral representation, we give another simple proof of an identity conjectured by Lacasse in the study of the PAC-Bayesian machine learning theory.
We present a very simple new bijective proof of Cayleys formula. The bijection is useful for the analysis of random trees, and we explain some of the ways in which it can be used to derive probabilistic identities, bounds, and growth procedures for s
uch trees. We also introduce a partial order on the degree sequences of rooted trees, and conjecture that it induces a stochastic partial order on heights of random rooted trees with given degrees.
An m x n cobweb network consists of n radial lines emanating from a center and connected by $m$ concentric n-sided polygons. A conjecture of Tan, Zhou and Yang for the resistance from center to perimeter of the cobweb is proved by extending the metho
d used by the above authors to derive formulae for m = 1, 2 and 3 and general n. The resistance of an m x (s+t+1) fan network from the apex to a point on the boundary distant s from the corner is also found.
In this paper, we confirm the following conjecture of Guo and Schlosser: for any odd integer $n>1$ and $M=(n+1)/2$ or $n-1$, $$ sum_{k=0}^{M}[4k-1]_{q^2}[4k-1]^2frac{(q^{-2};q^4)_k^4}{(q^4;q^4)_k^4}q^{4k}equiv (2q+2q^{-1}-1)[n]_{q^2}^4pmod{[n]_{q^2}^
4Phi_n(q^2)}, $$ where $[n]=[n]_q=(1-q^n)/(1-q),(a;q)_0=1,(a;q)_k=(1-a)(1-aq)cdots(1-aq^{k-1})$ for $kgeq 1$ and $Phi_n(q)$ denotes the $n$-th cyclotomic polynomial.
In this paper, by means of the classical Lagrange inversion formula, we establish a general nonlinear inverse relations which is a partial solution to the problem proposed in the paper [J. Wang, Nonlinear inverse relations for the Bell polynomials vi
a the Lagrange inversion formula, J. Integer Seq., Vol. 22 (2019), Article 19.3.8. (https://cs.uwaterloo.ca/journals/JIS/VOL22/Wang/wang53.pdf). As applications of this inverse relation, we not only find a short proof of another nonlinear inverse relation due to Birmajer et al., but also set up a few convolution identities concerning the Mina polynomials.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
