Concept
Combinatorial proof
Related publications (13)
Computational Imaging SPAD Cameras
Vision systems built around conventional image sensors have to read, encode and transmit large quantities of pixel information, a majority of which is redundant. As a result, new computational imaging sensor architectures were developed to preprocess the r ...
EPFL2023Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths
In this paper we study the moments of polynomials from the Askey scheme, and we focus on Askey-Wilson polynomials. More precisely, we give a combinatorial proof for the case where d = 0. Their values have already been computed by Kim and Stanton in 2015, h ...
ELECTRONIC JOURNAL OF COMBINATORICS2021A combinatorial proof of a sumset conjecture of Furstenberg
We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if is irrational and and are - and -invariant subsets of , respectively, then $\dim_\text{ ...
2021Heterogeneous combinatorial expression of Hoxd genes in single cells during limb development
Denis Duboule, Marion Leleu, Pierre Raymond Fabre
Background: Global analyses of gene expression during development reveal specific transcription patterns associated with the emergence of various cell types, tissues, and organs. These heterogeneous patterns are instrumental to ensure the proper formation ...
BMC2018Vector-Based 3D graphic statics (Part III): Designing with Combinatorial Equilibrium Modelling
Corentin Jean Dominique Fivet, Pierluigi D'Acunto
This paper presents an extension of the graphic-statics-based framework called Combinatorial Equilibrium Modelling (CEM). CEM allows for the generation of topologically and combinatorially different spatial equilibrium solutions in the early explorative de ...
IASS2016Homology of the three flag Hilbert Scheme
We prove the existence of an affine paving for the three-step flag Hilbert scheme that parametrizes flag of three 0-dimensional subschemes of length, respectively, n, n+1 and n+2 that are supported at the origin of the affine plane. This is done by showing ...
EPFL2016On vertices and facets of combinatorial 2-level polytopes
Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano
2-level polytopes naturally appear in several areas of mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. We investigate upper bounds on the product of the number of facets and the number ...
Springer2016Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms
Eva Bayer Fluckiger, Daniel Arnold Moldovan
We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be unimodular or defined o ...
Pacific Journal Mathematics2014Combinatorial necklace splitting
We give a new, combinatorial proof for the necklace splitting problem for two thieves using only Tucker's lemma (a combinatorial version of the Borsuk-Ulam theorem). We show how this method can be applied to obtain a related recent result of Simonyi and ev ...
American Mathematical Society2009