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A Generalized Diagonal Wythoff Nim

Urban Larsson (Institutionen för matematiska vetenskaper, matematik)
Integers (1553-1732). Vol. 12 (2012), G2, p. 1-24.
[Artikel, refereegranskad vetenskaplig]

The P-positions of the 2-pile take-away game of Wythoff Nim lie on two beams of slope (sqrt(5)+1)/2 and (sqrt(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 prove that for certain pairs (p, q) the P-positions are identical to those of Wythoff Nim, but for (p, q) = (1, 2) they do not even lie on two beams. By several experimental results, we conjecture a classification of all pairs (p, q) for which Wythoff Nim’s beams of P-positions transform via a certain splitting behavior, similar to that of going from 2-pile Nim to Wythoff Nim.

Nyckelord: Combinatorial game, splitting sequence, Wythoff Nim

Journal website: http://www.emis.de/journals/INTEGERS/

Denna post skapades 2012-08-21. Senast ändrad 2012-12-04.
CPL Pubid: 162375


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Institutionen för matematiska vetenskaper, matematik (2005-2016)


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