Publications related to Combinatorial proof

Computation 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 COMBINATORICS2021

A combinatorial proof of a sumset conjecture of Furstenberg

Florian Karl Richter

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if

\log r / \log s

is irrational and

X

and

Y

are

\times r

- and

\times s

-invariant subsets of

[0,1]

, respectively, then $\dim_\text{ ...

2021

Heterogeneous 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 ...

BMC2018

Vector-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 ...

IASS2016

On 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 ...

Springer2016

Hermitian 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 Mathematics2014

Combinatorial necklace splitting

Doemoetoer Palvoelgyi

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

Interference-Resilient Information Exchange

Rachid Guerraoui, Seth Gilbert

This paper presents an efficient protocol for reliably exchanging information in a single-hop, multi-channel radio network subject to unpredictable interference. We model the interference by an adversary that can simultaneously disrupt up to t of the C ava ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

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A combinatorial proof of a sumset conjecture of Furstenberg

Florian Karl Richter

We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if

\log r / \log s

is irrational and

X

and

Y

are

\times r

- and

\times s

-invariant subsets of

[0,1]

, respectively, then $\dim_\text{ ...

2021

Combinatorial proof

Computational Imaging SPAD Cameras

Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths

A combinatorial proof of a sumset conjecture of Furstenberg

Heterogeneous combinatorial expression of Hoxd genes in single cells during limb development

Vector-Based 3D graphic statics (Part III): Designing with Combinatorial Equilibrium Modelling

Homology of the three flag Hilbert Scheme

On vertices and facets of combinatorial 2-level polytopes

Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms

Combinatorial necklace splitting

Interference-Resilient Information Exchange

Graph Chatbot

Chat with Graph Search

A combinatorial proof of a sumset conjecture of Furstenberg

On vertices and facets of combinatorial 2-level polytopes

Vector-Based 3D graphic statics (Part III): Designing with Combinatorial Equilibrium Modelling

Interference-Resilient Information Exchange

Hermitian Categories, Extension Of Scalars And Systems Of Sesquilinear Forms

Combinatorial necklace splitting