#### Filter Results:

- Full text PDF available (22)

#### Publication Year

2005

2017

- This year (1)
- Last 5 years (13)
- Last 10 years (21)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Urban Larsson, Peter Hegarty, Aviezri S. Fraenkel
- Theor. Comput. Sci.
- 2011

We prove a recent conjecture of Duchêne and Rigo, stating that every complementary pair of homogeneous Beatty sequences represents the solution to an invariant impartial game. Here invariance means that each available move in a game can be played anywhere inside the game board. In fact, we establish such a result for a wider class of pairs of complementary… (More)

We study a variation of the combinatorial game of 2-pile Nim. Move as in 2-pile Nim but with the following constraint: Provided the previous player has just removed say x > 0 tokens from the pile with less tokens, the next player may remove x tokens from the pile with more tokens. But for each move, in “a strict sequence of previous player next player… (More)

- Andreas Baltz, Peter Hegarty, Jonas Knape, Urban Larsson, Tomasz Schoen
- Electr. J. Comb.
- 2005

If k is a positive integer, we say that a set A of positive integers is k-sum-free if there do not exist a, b, c in A such that a + b = kc. In particular we give a precise characterization of the structure of maximum sized k-sum-free sets in {1, . . . , n} for k ≥ 4 and n large.

- URBAN LARSSON
- 2011

The P-positions of the well-known 2-pile take-away game of Wythoff Nim lie on two ‘beams’ of slope √ 5+1 2 and √ 5−1 2 respectively. We study extensions to this game where a player may also remove simultaneously pt tokens from either of the piles and qt from the other, where p < q are given positive integers and where t ranges over the positive integers. We… (More)

We study permutations π of the natural numbers for which the numbers π(n) are chosen greedily under the restriction that the differences π(n)−n belong to a given (multi)subset M of Z for all n ∈ S, a given subset of N. Various combinatorial properties of such permutations (for quite general M and S) are exhibited and others conjectured. Our results… (More)

- Urban Larsson
- Electr. J. Comb.
- 2011

The 2-player impartial game of Wythoff Nim is played on two piles of tokens. A move consists in removing any number of tokens from precisely one of the piles or the same number of tokens from both piles. The winner is the player who removes the last token. We study this game with a blocking maneuver, that is, for each move, before the next player moves the… (More)

- Urban Larsson
- Theor. Comput. Sci.
- 2012

An invariant subtraction game is a 2-player impartial game defined by a set of invariant moves (k-tuples of non-negative integers) M. Given a position (another k-tuple) x = (x1, . . . , xk), each option is of the form (x1 − m1, . . . , xk − mk), where m = (m1, . . . ,mk) ∈ M (and where xi − mi ≥ 0, for all i). Two players alternate in moving and the player… (More)

- Urban Larsson, Johan Wästlund
- Electr. J. Comb.
- 2013

We study so-called invariant games played with a fixed number d of heaps of matches. A game is described by a finite list M of integer vectors of length d specifying the legal moves. A move consists in changing the current game-state by adding one of the vectors in M, provided all elements of the resulting vector are nonnegative. For instance, in a two-heap… (More)

Fix a positive integerm. The game ofm-Wythoff Nim (A.S. Fraenkel, 1982) is a well-known extension of Wythoff Nim, a.k.a ’Corner the Queen’. Its set of P -positions may be represented by a pair of increasing sequences of non-negative integers. It is well-known that these sequences are so-called complementary homogeneous Beatty sequences, that is they satisfy… (More)

- Urban Larsson
- J. Comb. Theory, Ser. A
- 2013

We study two-player take-away games whose outcomes emulate two-state one-dimensional cellular automata, such as Wolfram’s rules 60 and 110. Given an initial string consisting of a central data pattern and periodic left and right patterns, the rule 110 cellular automaton was recently proved Turing-complete by Matthew Cook. Hence, many questions regarding its… (More)