Related papers: Tree-Loop Duality Relation beyond simple poles
BCJ relation reveals a dual between color structures and kinematic structure and can be used to reduce the number of independent color-ordered amplitudes at tree level. Refer to the loop-level in Yang-Mills theory, we investigate the…
A central limit theorem for binary tree is numerically examined. Two types of central limit theorem for higher-order branches are formulated. A topological structure of a binary tree is expressed by a binary sequence, and the…
The tree share structure proposed by Dockins et al. is an elegant model for tracking disjoint ownership in concurrent separation logic, but decision procedures for tree shares are hard to implement due to a lack of a systematic theoretical…
A general outlook is presented on the study of multiloop topologies appearing for the first time at four loops. A unified description and representation of this family is provided, the so-called N$^4$MLT universal topology. Based on the…
We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the Subtree…
We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…
Rotation distance between rooted binary trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. We give an efficient,…
The treewidth boundedness problem for a logic asks for the existence of an upper bound on the treewidth of the models of a given formula in that logic. This problem is found to be undecidable for first order logic. We consider a…
In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…
There are three kinds of multiple polylogarithms; complex, finite and symmetric. The dualities for the complex and finite cases are known. In this paper, we present proofs of them via iterated integrals and its symmetric counterpart by a…
We present a set of one-loop integral coefficient relations in QCD. The unitarity method is useful for exposing one-loop amplitudes in terms of tree amplitudes. The coefficient relations are induced by tree-level BCJ amplitude relations. We…
We study linear relations among correlation functions on a lattice obtained from integration-by-parts identities. We use the framework of twisted cocycles and determine for a scalar theory a basis of correlation functions, in which all…
We construct and solve a complete system of differential equations for general tree-level inflation correlators with an arbitrary number of massive scalar exchanges and time-dependent couplings. Any massive tree correlators can be uniquely…
The multiple root loci among univariate polynomials of degree $n$ are indexed by partitions of $n$. We study these loci and their conormal varieties. The projectively dual varieties are joins of such loci where the partitions are hooks. Our…
A Bialgebra is a module over a ring that is both an associative algebra and a co-associative coalgebra with the product and coproduct additionally satisfying an appropriate commutative relationship. One application of Bialgebras is in the…
In this paper, we present a systematic derivation aimed at obtaining general expressions for on-shell recursion relations for tree-level open string amplitudes. Our approach involves applying the BCFW shift to an open string amplitude…
We derive dispersion relations for a system of identical particles confined in a two-dimensional annular harmonic well and which interact through a Yukawa potential, e.g., a dusty plasma ring. When the particles are in a single chain (i.e.,…
We study transport equations for quantum many-particle systems in terms of correlations by applying the general formalism developed in an earlier paper to exactly soluble electron-phonon models. The one-dimensional models considered are the…
This paper considers three different partition relations from partition calculus, two of which are pair relations and one of which is a triple relation. An examination of the first partition relation and the ramification argument used to…
We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…