TY - JOUR
T1 - The sprague-grundy functions of saturations of Misère Nim
AU - Irie, Yuki
N1 - Funding Information:
This work was partially supported by JSPS KAKENHI Grant Number JP20K14277. Part of the work was carried out at Chiba University.
Funding Information:
∗This work was partially supported by JSPS KAKENHI Grant work was carried out at Chiba University.
Publisher Copyright:
© The author.
PY - 2021
Y1 - 2021
N2 - We consider misère Nim as a normal-play game obtained from Nim by removing the terminal position. While explicit formulas are known for the Sprague-Grundy functions of Nim and Welter’s game, no explicit formula is known for that of misère Nim. All three of these games can be considered as position restrictions of Nim. What are the differences between them? We point out that Nim and Welter’s game are saturated, but misère Nim is not. Moreover, we present explicit formulas for the Sprague-Grundy functions of saturations of misère Nim, which are obtained from misère Nim by adjoining some moves.
AB - We consider misère Nim as a normal-play game obtained from Nim by removing the terminal position. While explicit formulas are known for the Sprague-Grundy functions of Nim and Welter’s game, no explicit formula is known for that of misère Nim. All three of these games can be considered as position restrictions of Nim. What are the differences between them? We point out that Nim and Welter’s game are saturated, but misère Nim is not. Moreover, we present explicit formulas for the Sprague-Grundy functions of saturations of misère Nim, which are obtained from misère Nim by adjoining some moves.
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U2 - 10.37236/8916
DO - 10.37236/8916
M3 - Article
AN - SCOPUS:85103075433
VL - 28
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
SN - 1077-8926
IS - 1
M1 - P1.58
ER -