Integral factorial ratios

Integral Ratios of Factorials and Algebraic Hypergeometric Functions

This is not immediately obvious (for example, this ratio of factorials is not a product of multinomial coefficients) but it is not hard to prove. The only proof I know proceeds by checking that the valuations vp(un) are non-negative for every prime p; an interpretation of un as counting natural objects or being dimensions of natural vector spaces is far from clear. As it turns out, the generati...

Direct path integral estimators for isotope fractionation ratios.

Fractionation of isotopes among distinct molecules or phases is a quantum effect which is often exploited to obtain insights on reaction mechanisms, biochemical, geochemical, and atmospheric phenomena. Accurate evaluation of isotope ratios in atomistic simulations is challenging, because one needs to perform a thermodynamic integration with respect to the isotope mass, along with time-consuming...

THE SUPER CATALAN NUMBERS S(m,m+ s) FOR s ≤ 3 AND SOME INTEGER FACTORIAL RATIOS

We give a combinatorial interpretation for the super Catalan number S(m,m + s) for s ≤ 3 using lattice paths and make an attempt at a combinatorial interpretation for s = 4. We also examine the integrality of some factorial ratios.

Factorial Design

Factorial Anova

But these experiments [2] will not give us any information about the dependence or independence of the two factors, namely study habit and home environment. In such cases, we resort to Factorial ANOVA which not only helps us to study the effect of two or more factors but also gives information about their dependence or independence in the same experiment. There are many types of factorial desig...