Related papers: Counting square free monomial cremona maps

We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon Diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs;…

This note presents some numerical examples worked out in order to show the reader how to implement, within a widely accessible computational setting, the methodology for achieving zero cancellation in linear multivariable systems discussed…

I present a numerical algorithm for direct evaluation of multiple Grassmann integrals. The approach is exact and suffers no Fermion sign problems. Memory requirements grow exponentially with the interaction range and the transverse size of…

We discuss the concept of Cremona contractible plane curves, with an historical account on the development of this subject. We then classify Cremona contractible unions of d > 11 lines in the plane.

We compute all dynamical degrees of monomial maps by interpreting them as mixed volumes of polytopes. By exploiting further the isomorphism between the polytope algebra of P. McMullen and the universal cohomology of complete toric…

Given a surface with boundary and some points on its boundary, a polygon diagram is a way to connect those points as vertices of non-overlapping polygons on the surface. Such polygon diagrams represent non-crossing permutations on a surface…

Cluster algorithms have been recently used to eliminate sign problems that plague Monte-Carlo methods in a variety of systems. In particular such algorithms can also be used to solve sign problems associated with the permutation of fermion…

The question of whether or not a given integral polynomial takes infinitely many square-free values has only been addressed unconditionally for polynomials of degree at most 3. We address this question, on average, for polynomials of…

We construct infinite cubefree binary words containing exponentially many distinct squares of length n. We also show that for every positive integer n, there is a cubefree binary square of length 2n.

The purpose of this paper is to present simple and fast methods for computing control points for polynomial curves and polynomial surfaces given explicitly in terms of polynomials (written as sums of monomials). We give recurrence formulae…

This note presents new results for the squarefree value sets of quartic polynomials over the integers.

We describe some regular techniques of calculating finite degree invariants of triple points free smooth plane curves $S^1 \to R^2$. They are a direct analog of similar techniques for knot invariants and are based on the calculus of {\em…

The aim of this paper is to provide an explicit basis of the miniversal deformation of a monomial curve defined by a free semigroup -- these curves make up a notable family of complete intersection monomial curves. First, we dispense a…

The generalized Hamming weights (GHWs) of a linear code C extend the concept of minimum distance, which is the minimum cardinality of the support of all one-dimensional subspaces of C, to the minimum cardinality of the support of all…

We introduce a Sinkhorn-type algorithm for producing quantum permutation matrices encoding symmetries of graphs. Our algorithm generates square matrices whose entries are orthogonal projections onto one-dimensional subspaces satisfying a…

We prove that any function with real-valued coefficients, whose input is 4 binary variables and whose output is a real number, is perfectly equivalent to a quadratic function whose input is 5 binary variables and is minimized over the new…

We prove that any group of cardinality at most the one of $\mathbb{C}$ is a quotient of any Cremona group of rank at least $4$. This provides a definitive answer to the question of what the quotients of Cremona groups can be. As a…

In this paper we consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology. Consider a real 2-dimensional compact surface $S$, and fix a number of points $F$ on its boundary. We ask: how many…

We construct Cremona transformations of P^3 with bidegrees (d,e), where d<e^2+1, e< d^2+1 and d,e> 0.

Simulating noninteracting fermion systems is a common task in computational many-body physics. In absence of translational symmetries, modeling free fermions on $N$ modes usually requires poly$(N)$ computational resources. While often…