30 citations · 56 across the 12 of their papers we have counts for
15 papers
Impartial geodetic building games on graphs
Bret J. Benesh, Dana C. Ernst, Marie Meyer +2
A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the set. The convex hull of a set of vertices…
Braid graphs in simply-laced triangle-free Coxeter systems are partial cubes
Fadi Awik, Jadyn Breland, Quentin Cadman +1
In this paper, we study the structure of braid graphs in simply-laced Coxeter systems. We prove that every reduced expression has a unique factorization as a product of so-called l…
The spectrum of nim-values for achievement games for generating finite groups
Bret J. Benesh, Dana C. Ernst, Nandor Sieben
We study an impartial achievement game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group.…
Impartial achievement games for generating nilpotent groups
Bret J. Benesh, Dana C. Ernst, Nandor Sieben
We study an impartial game introduced by Anderson and Harary. The game is played by two players who alternately choose previously-unselected elements of a finite group. The first p…
Impartial achievement games for generating generalized dihedral groups
Bret J. Benesh, Dana C. Ernst, Nandor Sieben
We study an impartial game introduced by Anderson and Harary. This game is played by two players who alternately choose previously-unselected elements of a finite group. The first…
On the number of commutation classes of the longest element in the symmetric group
Hugh Denoncourt, Dana C. Ernst, Dustin Story
Using the standard Coxeter presentation for the symmetric group , two reduced expressions for the same group element are said to be commutation equivalent if we can obtain one…