tailieunhanh - Báo cáo toán học: "Aviezri Fraenkel and Combinatorial Games"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Aviezri Fraenkel and Combinatorial Games. | Aviezri Fraenkel and Combinatorial Games Richard K. Guy Calgary Canada The subject of combinatorial games has like combinatorics itself been slow to hnd recognition with the mathematical establishment. Combinatorics is now on sure ground and combinatorial games is well on its way. This is in no small part due to the energy enthusiasm and insight of Aviezri Fraenkel who has linked combinatorial games with much else in mathematics graph theory 24 error-correcting codes 22 numeration systems 25 28 continued fractions 17 and especially complexity theory. The great variety in the difficulty of the vast range of combinatorial games has enabled him to exhibit the whole spectrum of complexity theory 18 27 55 He has also ascertained the status of many particular combinatorial games 34 diophantine games 60 the Grundy function 14 chess 40 and checkers 33 . His interest in games may well have been sparked by a classic paper of Coxeter 6 certainly he has long been fascinated by the relation between Beatty sequences . complementing sequences of integers on the one hand and Wythoff s Game 9 39 11 1 8 on the other. Wythoff s Game is played with two heaps from which players alternately take any number from one heap or equal numbers from each several of Aviezri s papers have been concerned with generalizations of this game 3 7 15 17 32 45 61 . He has written on a variety of individual games many of which are his own invention Nimbi 36 Nimhoff games 43 and Nim itself 4 Geography 50 Epidemiography 41 42 44 geodetic contraction games 35 Particles and Antiparticles 12 a deletion game 48 a new heap game 58 modular Nim sometimes called Kotzig s Nim 37 Multivision 26 partizan octal and subtraction games 38 and extensions of Conway s short games 52 . He has been especially interested in annihilation games 10 53 54 56 and in games using Cedric Smith s extension of the Sprague-Grundy theory to cover games in which there are possible draws through inhnite play 2 371-375 . He provided Conway