Related papers: Small Extended Formulations for Cyclic Polytopes

An algorithm for matrix factorization of polynomials was proposed in \cite{fomatati2022tensor} and it was shown that this algorithm produces better results than the standard method for factoring polynomials on the class of summand-reducible…

Closed form expressions for a multivector exponential and logarithm are presented in real Clifford geometric algebras Cl(p,q)when n=p+q=1 (complex and hyperbolic numbers) and n=2 (Hamilton, split and conectorine quaternions). Starting from…

In this paper an approach to generate multi-dimensionally consistent $N$-component systems is proposed. The approach starts from scalar multi-dimensionally consistent quadrilateral systems and makes use of the cyclic group. The obtained…

In this note we consider fractions of the form 1/m and their floating-point representation in various arithmetic bases. For instance, what is 1/7 in base 2005? And, what about 1/4? We give a simple algorithm to answer these questions. In…

Very recently, Galashin, Postnikov, and Williams introduced the notion of higher secondary polytopes, generalizing the secondary polytope of Gelfand, Kapranov, and Zelevinsky. Given an $n$-point configuration $\mathcal{A}$ in…

The Lasserre's reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $(1\leq d\leq D)$ can be expressed as functions of the areas and normal bi-vectors of the…

We give a simple diagrammatic algorithm for writing the chiral large $N$ expansion of intersecting Wilson loops in $2D$ $SU(N)$ and $U(N) $Yang Mills theory in terms of symmetric groups, generalizing the result of Gross and Taylor for…

We develop a graphical calculus for the microformal or thick morphisms introduced by Ted Voronov. This allows us to write the infinite series arising from pullbacks, compositions, and coordinate transformations of thick morphisms as sums…

We consider the diagonal limit of the conformal bootstrap in arbitrary dimensions and investigate the question if physical theories are given in terms of cyclic polytopes. Recently, it has been pointed out that in $d=1$, the geometric…

In 2010, A. Shpilka and I. Volkovich established a prominent result on the equivalence of polynomial factorization and identity testing. It follows from their result that a multilinear polynomial over the finite field of order 2 can be…

In this paper, we study the algebraic formula complexity of multiplying $d$ many $2\times 2$ matrices, denoted $\mathrm{IMM}_{d}$, and show that the well-known divide-and-conquer algorithm cannot be significantly improved at any depth, as…

This paper presents a means with time complexity of at worst O(n^3) to compute the discrete logarithm on cyclic finite groups of integers modulo p. The algorithm makes use of reduction of the problem to that of finding the concurrent zeros…

We improve the estimates in the restriction problem in dimension $n \ge 4$. To do so, we establish a weak version of a $k$-linear restriction estimate for any $k$. The exponents in this weak $k$-linear estimate are sharp for all $k$ and…

The FORTRAN code POLRAD 2.0 for radiative correction calculation in inclusive and semi-inclusive deep inelastic scattering of polarized leptons by polarized nucleons and nuclei is described. Its theoretical basis, structure and algorithms…

In this paper, we compute the first set of ${\cal O}(\alpha_s^2)$ corrections to semi-inclusive deep inelastic scattering structure functions. We start by studying the impact of the contribution of the partonic subprocesses that open at…

We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way. Many of them are permutation polynomials of large indices.

Recently O. Pechenik studied the cyclic sieving of increasing tableaux of shape $2\times n$, and obtained a polynomial on the major index of these tableaux, which is a $q$-analogue of refined small Schr\"{o}der numbers. We define…

We present a coordinate space version of the factorization formula for the connected tree part of the chronological products. We consider a general framework and then we apply it for the QCD case.

We give an example of a one dimensional foliation $\cal F$ of degree two in a Zariski open set of a four dimensional weighted projective space which has only an enumerable set of algebraic leaves. These are defined over rational numbers and…

From a detailed analysis of cone-jet cross sections in effective field theory, we obtain novel factorization theorems which separate the physics associated with different energy scales present in such processes. The relevant low-energy…