Gabriel F. Lipnik

activity

20212023

most citedAsymptotic Analysis of q-Recursive Sequences

6 citations · 15 across the 6 of their papers we have counts for

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Showing 2022Show all

4 papers · 1 filter

math.CO2022★ 2 cited

Exponentially Larger Affine and Projective Caps

Christian Elsholtz, Gabriel F. Lipnik

In spite of a recent breakthrough on upper bounds of the size of cap sets (by Croot, Lev and Pach (2017) and Ellenberg and Gijswijt (2017)), the classical cap set constructions had…

math.NT2022★ 2 cited

Large Subsets of $Z_{m}^{n}$ without Arithmetic Progressions

Christian Elsholtz, Benjamin Klahn, Gabriel F. Lipnik

For integers $m$ and $n$ , we study the problem of finding good lower bounds for the size of progression-free sets in $(Z_{m}^{n}, +)$ . Let $r_{k} (Z_{m}^{n})$ denot…

math.NT2022★ 5 cited

A Central Limit Theorem for Integer Partitions into Small Powers

Gabriel F. Lipnik, Manfred G. Madritsch, Robert F. Tichy

The study of the well-known partition function $p (n)$ counting the number of solutions to $n = a_{1} + \dots + a_{ℓ}$ with integers $1 \leq a_{1} \leq \dots \leq a_{ℓ}$ has a…

math.CO2022

A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations

Clemens Heuberger, Daniel Krenn, Gabriel F. Lipnik

In this note, we precisely elaborate the connection between recognisable series (in the sense of Berstel and Reutenauer) and $q$ -regular sequences (in the sense of Allouche and Sha…

Exponentially Larger Affine and Projective Caps

Large Subsets of Zmn​ without Arithmetic Progressions

A Central Limit Theorem for Integer Partitions into Small Powers

A Note on the Relation between Recognisable Series and Regular Sequences, and their Minimal Linear Representations

Large Subsets of $Z_{m}^{n}$ without Arithmetic Progressions