Completing Multi‐Latin Rectangles via Factors With Prescribed Degrees in Bipartite Graphs
ABSTRACT Let Q be an n × n array whose top left r × s sub‐array L is filled with a set of k different symbols such that each cell of L contains λ symbols. In this note, we find conditions under which each empty cell of Q can be filled with λ symbols in such a way that the total number of occurrences of each symbol is prescribed and that each symbol ...
Amin Bahmanian
wiley +1 more source
Analyzing Boltzmann Samplers for Bose-Einstein Condensates with Dirichlet Generating Functions
Boltzmann sampling is commonly used to uniformly sample objects of a particular size from large combinatorial sets. For this technique to be effective, one needs to prove that (1) the sampling procedure is efficient and (2) objects of the desired size ...
Bernstein, Megan +2 more
core +1 more source
New Difference Triangle Sets by a Field‐Programmable Gate Array‐Based Search Technique
ABSTRACT We provide some difference triangle sets with scopes that improve upon the best known values. These are found with purpose‐built digital circuits realized with field‐programmable gate arrays (FPGAs) rather than software algorithms running on general‐purpose processors.
Mohannad Shehadeh +2 more
wiley +1 more source
On positivity of Ehrhart polynomials
Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart ...
Alexander Postnikov +48 more
core +1 more source
Polynomially oscillatory multipliers on Gelfand–Shilov spaces
Abstract We study continuity of the multiplier operator eiq$\text{e}^{\text{i} q}$ acting on Gelfand–Shilov spaces, where q$q$ is a polynomial on Rd$\mathbf {R}^{d}$ of degree at least two with real coefficients. In the parameter quadrant for the spaces, we identify a wedge that depends on the polynomial degree for which the operator is continuous.
Alexandre Arias Junior, Patrik Wahlberg
wiley +1 more source
The combinatorics of scattering in layered media [PDF]
Reflection and transmission of waves in piecewise constant layered media are important in various imaging modalities and have been studied extensively. Despite this, no exact time domain formulas for the Green's functions have been established.
Gibson, Peter C.
core
On the Stability Barrier of Hermite Type Discretizations of Advection Equations
ABSTRACT We establish a stability barrier for a class of high‐order Hermite‐type discretization of 1D advection equations underlying the hybrid‐variable (HV) and active flux (AF) methods. These methods approximate both cell averages and nodal solutions and evolve them in time simultaneously.
Xianyi Zeng
wiley +1 more source
Perspectives for proof unwinding by programming languages techniques [PDF]
In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory.
Ilik, Danko
core +3 more sources
A Refined Graph Container Lemma and Applications to the Hard‐Core Model on Bipartite Expanders
ABSTRACT We establish a refined version of a graph container lemma due to Galvin and discuss several applications related to the hard‐core model on bipartite expander graphs. Given a graph G$$ G $$ and λ>0$$ \lambda >0 $$, the hard‐core model on G$$ G $$ at activity λ$$ \lambda $$ is the probability distribution μG,λ$$ {\mu}_{G,\lambda } $$ on ...
Matthew Jenssen +2 more
wiley +1 more source
Combinatorics: The Mathematics of Fair Thieves and Sophisticated Forgetters
Mathematics is the most logical and unbiased scientific field there is. What is true in mathematics today will forever stay true, and mathematical arguments will always clearly indicate which side “wins”. These are some of the characteristics of mathematics that I have liked very much since I was young.
openaire +1 more source

