Related papers: On the Thom-Boardman Symbols for Polynomial Multip…
The purpose of this expository note is to give the proof of a theorem of Bourgain with some additional details and updated notation. The theorem first appeared as an appendix to the breakthrough paper by Friedgut, \emph{Sharp Thresholds of…
Building on the results of [1,2], we study the resurgence of $q$-Pochhammer symbols and determine their summability and quantum modularity properties. We construct a new, infinite family of pairs of modular resurgent series from the…
The complexity of Philip Wolfe's method for the minimum Euclidean-norm point problem over a convex polytope has remained unknown since he proposed the method in 1974. The method is important because it is used as a subroutine for one of the…
We consider a refinement of the partition function of graph homomorphisms and present a quasi-polynomial algorithm to compute it in a certain domain. As a corollary, we obtain quasi-polynomial algorithms for computing partition functions…
A formula for the number of monic irreducible self-reciprocal polynomials, of a given degree over a finite field, was given by Carlitz in 1967. In 2011 Ahmadi showed that Carlitz's formula extends, essentially without change, to a count of…
This paper studies the restriction multiplicities of half-diagram modules for the partition algebra and their geometric interpretations. By specializing the Bowman-De Visscher-Orellana formula [BVC, Theorem 4.3] for restriction…
We initiate a systematic framework for the analysis of analytic properties of finite Feynman integrals that are multiple polylogarithms. Based on the Feynman parameter representation in complex projective space, we make a complete…
We extend an algorithm suggested in 1858 by Sylvester and implemented in 1860 by Cayley for a problem of double partitions and apply it to derivation of explicit expressions for coefficients of the Gaussian polynomials through convolution…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…
We show that the Borel sums of the Voros symbols considered in the theory of exact WKB analysis arise naturally as Fock-Goncharov coordinates of framed $PGL_2(\mathbb{C})$-local systems on a marked bordered surface. Using this result, we…
We define complex cobordism realizations of cohomological Thom polynomials and study their existence, uniqueness and other features. We show that problem is non-trivial on the example of $\Sigma^1$ singularity.
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
Firstly, for a general graph, we find a recursion formula on the number of Hamiltonian cycles and one on cycles. By this result, we give some new polynomial invariants. Secondly, we give a condition to tell whether a polynomial defined by…
We consider the two-variable interlace polynomial introduced by Arratia, Bollobas and Sorkin (2004). We develop graph transformations which allow us to derive point-to-point reductions for the interlace polynomial. Exploiting these…
A description of Orthogonal Tensor Hermite Polynomials in 3-D is presented. These polynomials, as introduced by Grad in 1949 [1], can be used to obtain a series solution to the Boltzmann Transport Equation. The properties that are explored…
We study scalar multivariate non-stationary subdivision schemes with a general dilation matrix. We characterize the capability of such schemes to reproduce exponential polynomials in terms of simple algebraic conditions on their symbols.…
The Jones polynomial, discovered in 1984, is an important knot invariant in topology. Among its many connections to various mathematical and physical areas, it is known (due to Witten) to be intimately connected to Topological Quantum Field…
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…
We introduce the notion of flag Bott-Samelson variety as a generalization of Bott-Samelson variety and flag variety. Using a birational morphism from an appropriate Bott-Samelson variety to a flag Bott-Samelson variety, we compute…
For an odd prime $p$, we study the image of the Thom map from Brown-Peterson cohomology of $BPU_n$ to the ordinary cohomology in dimensions $0\leq i\leq 2p+2$, where $BPU_n$ is the classifying space of the projective unitary group $PU_n$.…