DeepAI

# A Cycle Joining Construction of the Prefer-Max De Bruijn Sequence

We propose a novel construction for the well-known prefer-max De Bruijn sequence, based on the cycle joining technique. We further show that the construction implies known results from the literature in a straightforward manner. First, it implies the correctness of the onion theorem, stating that, effectively, the reverse of prefer-max is in fact an infinite De Bruijn sequence. Second, it implies the correctness of recently discovered shift rules for prefer-max, prefer-min, and their reversals. Lastly, it forms an alternative proof for the seminal FKM-theorem.

• 3 publications
• 6 publications
• 10 publications
06/10/2019

### On Embedding De Bruijn Sequences by Increasing the Alphabet Size

The generalization of De Bruijn sequences to infinite sequences with res...
07/26/2018

### A new proof of Grinberg Theorem based on cycle bases

Grinberg Theorem, a necessary condition only for planar Hamiltonian grap...
01/30/2018

### An Efficient Generalized Shift-Rule for the Prefer-Max De Bruijn Sequence

One of the fundamental ways to construct De Bruijn sequences is by using...
04/19/2019

### Cantor-Bernstein implies Excluded Middle

We prove in constructive logic that the statement of the Cantor-Bernstei...
05/07/2018

### A Combinatorial Game and an Efficiently Computable Shift Rule for the Prefer Max De Bruijn Sequence

We present a two-player combinatorial game over a k-ary shift-register a...
01/17/2022

### Numerical approaches for investigating quasiconvexity in the context of Morrey's conjecture

Deciding whether a given function is quasiconvex is generally a difficul...