Related papers: Real Grassmann Polylogarithms and Chern Classes
Let $\pi: {\mathbb C}_g \to {\mathbb M}_g$ be the universal family of compact Riemann surfaces of genus $g \geq 1$. We introduce a real-valued function on the moduli space ${\mathbb M}_g$ and compute the first and the second variations of…
Developing explicit pseudorandom generators (PRGs) for prominent categories of Boolean functions is a key focus in computational complexity theory. In this paper, we investigate the PRGs against the functions of degree-$d$ polynomial…
In this paper, we present a new real-valued Appell-type polynomial family $A_n^{(k)}(m,x), $ every member of which is expressed by mean of a generalized hypergeometric function. The generating exponential function of this type of…
The existence of bivariant Chern classes was conjectured by W.Fulton and R.MacPherson and proved by J.P.Brasselet for cellular morphisms of analytic varieties. In this paper we show that restricted to morphisms whose target varieties are…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
Quiver Grassmannians and quiver flags are natural generalisations of usual Grassmannians and flags. They arise in the study of quiver representations and Hall algebras. In general, they are projective varieties which are neither smooth nor…
We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…
The Pimenov algebra with two generators is defined and some of its properties are shown. Some exact matrix over the Pimenov algebra representations of the motions group of Galilean plane (the Galilean group) are considered. A geometric…
The Chern-Schwartz-MacPherson (CSM) and motivic Chern (mC) classes of Schubert cells in a Grassmannian are one parameter deformations of the fundamental classes of the Schubert varieties in cohomology and K-theory respectively. Like the…
We give explicit formulas for the Chern-Schwartz-MacPherson classes of all Schubert varieties in the Grassmannian of $d$-planes in a vector space, and conjecture that these classes are effective. We prove this is the case for (very) small…
Michael Gromov has recently initiated what he calls ``symbolic algebraic geometry", in which objects are proalgebraic varieties: a proalgebraic variety is by definition the projective limit of a projective system of algebraic varieties. In…
The multi-point Taylor polynomial, which is the general, unique and of minimum degree ($mk+m-1$) polynomial $P_{k,m}(x)$ which interpolates a function's derivatives in multiple points is presented in its explicit form. A proof that this…
A Golomb ruler is a sequence of integers whose pairwise differences, or equivalently pairwise sums, are all distinct. This definition has been generalized in various ways to allow for sums of h integers, or to allow up to g repetitions of a…
Some aspects of differential and integral calculi on generalized grassmann (paragrassmann) algebras are considered. The integration over paragrassmann variables is applied to evaluate the partition function for the $Z_{p+1}$ Potts model on…
The M-polynomial, introduced by Deutsch and Klav\v{z}ar in 2015, provides a unifying algebraic framework for the computation of numerous degree-based topological indices such as the Zagreb, Randic, harmonic, and forgotten indices. Despite…
We give a general method to construct a complete set of linearly independent Casimir operators of a Lie algebra with rank N. For a Casimir operator of degree p, this will be provided by an explicit calculation of its symmetric coefficients…
In these lectures I discuss Feynman graphs and the associated Feynman integrals. Of particular interest are the classes functions, which appear in the evaluation of Feynman integrals. The most prominent class of functions is given by…
A new relation between Prym varieties of arbitrary morphisms of algebraic curves and integrable systems is discovered. The action of maximal commutative subalgebras of the formal loop algebra of GL(n) defined on certain infinite-dimensional…
There are two widely used models for the Grassmannian $\operatorname{Gr}(k,n)$, as the set of equivalence classes of orthogonal matrices $\operatorname{O}(n)/(\operatorname{O}(k) \times \operatorname{O}(n-k))$, and as the set of trace-$k$…
In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In [2] and [3] the authors generalized…