5 citations · 8 across the 11 of their papers we have counts for
13 papers
Impartial geodetic removing 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 subset. The convex hull of a set of vertic…
Reducing the Incentive to Tank: The Ex Post Gold Plan
Bret Benesh
Many recent proposals for reducing tanking in draft lotteries share a common structure: losses improve draft position early in the season while wins improve draft position later. W…
Impartial removing games on grid 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 subset. The convex hull of a set of vertic…
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…
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…
Bounds on the number of conjugacy classes of the symmetric and alternating groups
Bret Benesh, Cong Tuan Son Van
Let be a finite group with Sylow subgroups , and let denote the number of conjugacy classes of . Pyber asked if for a…
Three-person impartial avoidance games for generating finite cyclic, dihedral, and nilpotent groups
Bret Benesh, Marisa Gaetz
We study a three-player variation of the impartial avoidance game introduced by Anderson and Harary. Three players take turns selecting previously-unselected elements of a finite g…
Group bases for some solvable groups and semidirect products
Bret Benesh, Jason Lutz
A set is a basis for a vector space if every element of can be uniquely written as a linear combination of the elements of . There is a similar definition of a basis…
On two questions by Finch and Jones about perfect order subset groups
Bret J. Benesh
A finite group G is said to be a POS-group if the number of elements of every order occurring in G divides |G|. We answer two questions by Finch and Jones by providing an infinite…
Impartial avoidance and achievement games for generating symmetric and alternating groups
Bret J. Benesh, Dana C. Ernst, Nandor Sieben
We study two impartial games introduced by Anderson and Harary. Both games are played by two players who alternately select previously-unselected elements of a finite group. The fi…
Impartial avoidance games for generating finite groups
Bret J. Benesh, Dana C. Ernst, Nandor Sieben
We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. T…