A Generalized Index of Fractionalization

A Generalized Major Index Statistic

Inspired by the k-inversion statistic for LLT polynomials, we define a k-inversion number and k-descent set for words. Using these, we define a new statistic on words, called the k-major index, that interpolates between the major index and inversion number. We give a bijective proof that the k-major index is equi-distributed with the major index, generalizing a classical result of Foata and red...

A generalized Morse index theorem

In this paper, we prove a Morse index theorem for the index form of even order linear Hamiltonian systems on the closed interval with reasonable self-adjoint boundary conditions. The highest order term is assumed to be nondegenerate.

On generalized atom-bond connectivity index of cacti

The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for  ABCa index for cacti of order $n$ ...

Value Fractionalization: A New Measure of Diversity

A generalized cost Malmquist index to compare the productivities of units with negative data in DEA

In some data envelopment analysis (DEA) applications, some inputs of DMUs have negative values with positive cost. This paper generalizes the global cost Malmquist productivity index to compare the productivity of dierent DMUs with negative inputs in any two periods of times under variable returns to scale (VRS) technology, and then the generalized index is decomposed to several components. The...