We develop structural insights into the Littlewood-Richardson graph, whose number of vertices equals the Littlewood-Richardson coefficient cνλ,μ for given partitions λ, μ and ν. This graph was first introduced in [BI12], where its connectedness was proved. Our insights are useful for the design of algorithms for computing the Littlewood-Richardson coefficient: We design an algorithm for the exa...

Next-to-MHV one-loop amplitudes in N = 4 gauge theory can be written as a linear combination of known multivalued functions, called scalar box functions, with coefficients that are rational functions. We consider the localization of these coefficients in twistor space and prove that all of them are localized on a plane. The proof is done by studying the action of differential operators that tes...

can be found in closed form by means of certain transformations on generating functions and the extraction of coefficients (see the end of section 3) suggested by Ira Gessel, and they comment: “He [Gessel] attributes this elegant technique, the ‘method of coefficients,’ to G. P. Egorychev.” Actually, in his book Integral Representation and Computation of Combinatorial Sums, Egorychev [4] (see [...

The authors verify the conjecture that a conjugate pair of zeros can be factored from a polynomial with nonnegative coefficients so that the resulting polynomial still has nonnegative coefficients. The conjecture was originally posed by A. Rigler, S. Trimble, and R. Varga arising out of their work on the Beauzamy-Enflo generalization of Jensen's inequality. The conjecture was also made independ...