5 papers
The triple rendezvous time of a synchronizing automaton can be floor(4n/3)
Enkai Zhang
For every , we construct a strongly connected synchronizing automaton with two input letters and states whose shortest word merging some three distinct states has length…
Exact diameter compression for four-point sumset cardinalities
Enkai Zhang
The least interval diameter needed to realize every attainable cardinality of an -fold sumset of a four-element integer set is for and $…
The additive-square-free spectrum below 139
Enkai Zhang
For a finite real alphabet , let be the supremum of the lengths of words over containing no two adjacent nonempty blocks of equal length and equal sum. We classify al…
Density regions, integer certificates and packing colorings of distance graphs
Enkai Zhang
We study simultaneous color densities in packing colorings of integer distance graphs. For , we determine several exact density regions and prove that colors through $7…
Sharp order-preserving integer models for short additive equalities
Enkai Zhang
We ask how small an increasing integer model of a finite real set can be while preserving all equalities between equal-length sums of at most elements, with repetitions allowed…