Publications associées à Packing the Boolean lattice with copies of a poset

Mean value theorems for collections of lattices with a prescribed group of symmetries

Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

EPFL2024

Additive and geometric transversality of fractal sets in the integers

Florian Karl Richter

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

GLOBALLY plus -REGULAR VARIETIES AND THE MINIMAL MODEL PROGRAM FOR THREEFOLDS IN MIXED CHARACTERISTIC

Zsolt Patakfalvi, Joseph Allen Waldron

We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global F-regularity to mixed characteristic and identify certain stable sections of adjoint lin ...

SPRINGER HEIDELBERG2023

The Lang-Trotter conjecture for products of non-CM elliptic curves

Vlad Serban

Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over Q and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study the analogous que ...

SPRINGER2022

On rationally connected varieties over C1 fields of characteristic 0

Marta Pieropan

We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...

MATHEMATICAL SCIENCE PUBL2022

Idempotents in the endomorphism algebra of a finite lattice

Jacques Thévenaz, Serge Bouc

We give a direct construction of a specific central idempotent in the endomorphism algebra of a finite lattice T. This idempotent is associated with all possible sublattices of T which are totally ordered. A generalization is considered in a conjectural fa ...

2022

A simple proof for a forbidden subposet problem

Abhishek Methuku

The poset Y-k,Y-2 consists of k + 2 distinct elements x(1), x(2), ..., x(k), y(1), y(2), such that x(1)

ELECTRONIC JOURNAL OF COMBINATORICS2020

New dense superball packings in three dimensions

Maria Margarethe Dostert

We construct a new family of lattice packings for superballs in three dimensions (unit balls for the l(3)(p) norm) with p epsilon (1, 1.58]. We conjecture that the family also exists for p epsilon (1.58, log(2) 3 = 1.5849625 ...]. Like in the densest latti ...

WALTER DE GRUYTER GMBH2020

Proximity Results and Faster Algorithms for Integer Programming Using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b, x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m), and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2020

On the Number of Containments in P-free Families

Abhishek Methuku

A subfamily {F-1, F-2, ..., F-vertical bar P vertical bar} subset of F is a copy of the poset P if there exists a bijection i : P -> {F-1, F-2, ..., F-vertical bar P vertical bar}, such that p

Springer2019

Forbidden induced subposets of given height

Istvan Tomon

Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

Nested Convex Bodies are Chaseable

Marek Elias

In the Convex Body Chasing problem, we are given an initial point v0. Rd and an online sequence of n convex bodies F1,..., Fn. When we receive Ft, we are required to move inside Ft. Our goal is to minimize the total distance traveled. This fundamental onli ...

SPRINGER2020

Construction of Polar Codes With Sublinear Complexity

Rüdiger Urbanke, Seyed Hamed Hassani, Marco Mondelli

Consider the problem of constructing a polar code of block length N for a given transmission channel W. Previous approaches require one to compute the reliability of the N synthetic channels and then use only those that are sufficiently reliable. However, ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Characterization of local morphology and availability of triple-phase boundaries in solid oxide cell electrodes

Jan Van Herle, Marco Cantoni, Arata Nakajo, Pierre Burdet, Giorgio Rinaldi

The performance of solid oxide cells is known to be dependent upon the density of three phase boundaries (TPB), but the potential for improving their effective electrocatalytic activity by morphological adjustments is imprecisely known. A spilling algorith ...

2019

Almost tiling of the Boolean lattice with copies of a poset

Istvan Tomon

Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...

ELECTRONIC JOURNAL OF COMBINATORICS2018

Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma

Friedrich Eisenbrand

We consider integer programming problems in standard form max{c(T)x : Ax = b; x >= 0, x is an element of Z(n)} where A is an element of Z(mxn), b is an element of Z(m) and c is an element of Z(n). We show that such an integer program can be solved in time ...

ASSOC COMPUTING MACHINERY2018

Counting Intersecting and Pairs of Cross-Intersecting Families

Andrei Kupavskii

A family of subsets of {1, ... , n} is called intersecting if any two of its sets intersect. A classical result in extremal combinatorics due to Erdos, Ko and Rado determines the maximum size of an intersecting family of k-subsets of {1, ... , n}. In this ...

Cambridge Univ Press2018

Distinct distances on regular varieties over finite fields

Van Thang Pham

In this paper we study some generalized versions of a recent result due to Covert, Koh, and Pi (2015). More precisely, we prove that if a subset in a regular variety satisfies vertical bar epsilon vertical bar >> q(d-1/2 + 1/k-1), then Delta(k,F)(epsilon) ...

Elsevier2017

Early-stage decision making approach for the selection of optimally integrated biorefinery processes

François Maréchal, Adriano Viana Ensinas, Ayse Dilan Celebi, Shivom Sharma

Lignocellulosic biorefineries are the best non-petroleum alternatives for a sustainable development. In the biorefinery process design, it is important to implement an algorithm that allows the systematic generation and the evaluation of energy conversion ...

2017

Multiple-field based code generator and decoder for communications systems

Lorenz Minder, Mohammad Amin Shokrollahi

A method of encoding data for transmission from a source to a destination over a communications channel is provided. The method operates on an ordered set of input symbols and includes generating a plurality of redundant symbols from the input symbols base ...

2016