6 citations · 15 across the 6 of their papers we have counts for
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A Local Limit Theorem for Integer Partitions into Small Powers
Gabriel F. Lipnik, Manfred G. Madritsch, Robert F. Tichy
The investigation of partitions of integers plays an important role in combinatorics and number theory. Among the many variations, partitions into powers were of recent int…
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…
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 -regular sequences (in the sense of Allouche and Sha…
Asymptotic Analysis of q-Recursive Sequences
Clemens Heuberger, Daniel Krenn, Gabriel F. Lipnik
For an integer , a -recursive sequence is defined by recurrence relations on subsequences of indices modulo some powers of~. In this article, -recursive sequences a…