6 citations · 11 across the 11 of their papers we have counts for
15 papers
Sprague-Grundy Function of Matroids and Related Hypergraphs
Endre Boros, Vladimir Gurvich, Nhan Bao Ho +2
We consider a generalization of the classical game of called hypergraph . Given a hypergraph $\cH$ on the ground set of piles of stones, two p…
Sprague-Grundy Function of Symmetric Hypergraphs
Endre Boros, Vladimir Gurvich, Nhan Bao Ho +2
We consider a generalization of the classical game of called hypergraph . Given a hypergraph $\cH$ on the ground set of piles of stones, two p…
The Sprague-Grundy function for some nearly disjunctive sums of Nim and Silver Dollar games
Graham Farr, Nhan Bao Ho
We introduce and analyse an extension of the disjunctive sum operation on some classical impartial games. Whereas the disjunctive sum describes positions formed from independent su…
Tetris Hypergraphs and Combinations of Impartial Games
Endre Boros, Vladimir Gurvich, Nhan Bao Ho +2
The Sprague-Grundy (SG) theory reduces the sum of impartial games to the classical game of . We generalize the concept of sum and introduce $\cH$-combinations of impartial gam…
Slow -Nim
Vladimir Gurvich, Nhan Bao Ho
Given piles of tokens and a positive integer , we study the following two impartial combinatorial games Nim and Nim. In the first (resp. s…
On tame, pet, domestic, and miserable impartial games
Vladimir Gurvich, Nhan Bao Ho
Playing impartial games under the normal and misere conventions may differ a lot. However, there are also many "exceptions" for which the normal and misere plays are very similar.…
On the Sprague-Grundy function of Exact -Nim
Endre Boros, Vladimir Gurvich, Nhan Bao Ho +2
Moore's generalization of the game of {\sc Nim} is played as follows. Let and be two integers such that . Given piles of tokens, two players move alter…
Three-pile Sharing Nim and the quadratic time winning strategy
Nhan Bao Ho
We study a variant of 3-pile Nim in which a move consists of taking tokens from one pile and, instead of removing then, topping up on a smaller pile provided that the destination p…
On the Sprague-Grundy Function of Tetris Extensions of Proper {\sc Nim}
Endre Boros, Vladimir Gurvich, Nhan Bao Ho +1
Given a hypergraph $\cH \subseteq 2^I \setminus \{\emptyset\}$ on the ground set , we assign to each a nonnegative integer , that is a pile of…
When are translations of P-positions of Wythoff's game P-positions?
Aviezri S. Fraenkel, Nhan Bao Ho
We study the problem whether there exist variants of {\sc Wythoff}'s game whose -positions, except for a finite number, are obtained from those of {\sc Wythoff}'s game by adding…
Variants of Wythoff's game translating its P-positions
Nhan Bao Ho
We introduce a restriction of Wythoff's game, which we call F-Wythoff, in which the integer ratio of entries must not change if an equal number of tokens are removed from both pile…
Two variants of Wythoff's game preserving its P-positions
Nhan Bao Ho
We present two variants of Wythoff's game. The first game is a restriction of Wythoff's game in which removing tokens from the smaller pile is not allowed if the two entries are no…
A restriction of Euclid
Grant Cairns, Nhan Bao Ho
Euclid is a well known two-player impartial combinatorial game. A position in Euclid is a pair of positive integers and the players move alternately by subtracting a positive integ…
The game Max-Welter
Nhan Bao Ho
On a semi-infinite strip of squares rightward numbered with at most one coin in each square, in Welter's game, two players alternately move a coin to an empty squ…
On the expansion of three-element subtraction sets
Nhan Bao Ho
We study the periodicity of nim-sequences for subtraction games having subtraction sets with three elements. In particular, we give solutions in several cases, and we describe how…