𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Generalized Mahonian Statistic on Absorption Ring Mappings

✍ Scribed by Don Rawlings

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
279 KB
Volume
79
Category
Article
ISSN
0097-3165

No coin nor oath required. For personal study only.

✦ Synopsis

Based on a coin-tossing scheme, a generalized Mahonian statistic is defined on absorption ring mappings and applied in obtaining combinatorial interpretations of the coefficient of q j in the expansion of > k i=1 (1+q+q 2 + } } } +q m i ). In the permutation case, the statistic coincides with one studied by Han that specializes many known Mahonian statistics.

1997 Academic Press _ # Sn q s(_) =[n]!. Besides inv and maj, many new Mahonian statistics have recently been discovered (see Foata and Zeilberger [6], Galovich and White [7], Han [8,9], Kadell [10], Liang and Wachs [12], Rawlings [17], and Zeilberger and Bressoud [24]).

Using a scheme based on Bernoulli trials, a generalized Mahonian statistic is herein defined on a set of functions called absorption ring mappings.

πŸ“œ SIMILAR VOLUMES

On the generalization error by a layered
On the generalization error by a layered statistical model with Bayesian estimation
✍ Sumio Watanabe πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 287 KB πŸ‘ 1 views

When a statistical estimation is carried out with a model that has layered parameters such as a neural network, the behavior of the generalization error and the optimum model design method are unknown, since unlike the regular model, the asymptotic behavior of the estimated parameters is not clear.

Novel Molecular Resist Based on a First
Novel Molecular Resist Based on a First Generation Dendrimer Possessing Furan Rings
✍ Hajime Mori; Eisaku Nomura; Asao Hosoda; Yasuhito Miyake; Hisaji Taniguchi πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 165 KB

## Abstract **Summary:** A novel chemically amplified negative‐tone molecular resist for electron‐beam (EB) lithography was developed. The base matrix had six furan rings as a reactive functional group at its terminal. The resist containing the matrix, a crosslinker and a photoacid generator worked

A New State Estimation Method For A Quan
A New State Estimation Method For A Quantized Stochastic Sound System Based On A Generalized Statistical Linearization
✍ E. Uchino; M. Ohta; H. Takata πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 334 KB

This paper describes a new method of state estimation for a stochastic sound system when the observation system is non-linear and quantized. The method is based on a generalized statistical linearization technique, with use of the two-sided Laplace transform. The non-linear quantized observation sys