149,253 research outputs found
The use of blocking sets in Galois geometries and in related research areas
Blocking sets play a central role in Galois geometries. Besides their intrinsic geometrical importance, the importance of blocking sets also arises from the use of blocking sets for the solution of many other geometrical problems, and problems in related research areas. This article focusses on these applications to motivate researchers to investigate blocking sets, and to motivate researchers to investigate the problems that can be solved by using blocking sets. By showing the many applications on blocking sets, we also wish to prove that researchers who improve results on blocking sets in fact open the door to improvements on the solution of many other problems
Blocking Wythoff Nim
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 previous player may declare
at most a predetermined number, , of the options as forbidden.
When the next player has moved, any blocking maneuver is forgotten and does not
have any further impact on the game. We resolve the winning strategy of this
game for and and, supported by computer simulations, state
conjectures of the asymptotic `behavior' of the -positions for the
respective games when .Comment: 14 pages, 1 Figur
Combinatorial problems in finite geometry and lacunary polynomials
We describe some combinatorial problems in finite projective planes and
indicate how R\'edei's theory of lacunary polynomials can be applied to them
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