scholarly journals Transversals in hypergraphs through a new combinatorial game

2022 ◽  
Vol 48 (16) ◽  
Author(s):  
Wilder Mendes ◽  
Simone Dantas ◽  
Sylvain Gravier
Keyword(s):  
Integers ◽  
2009 ◽  
Vol 9 (6) ◽  
Author(s):  
Urban Larsson

AbstractWe study a variation of the combinatorial game of 2-pile Nim. Move as in 2-pile Nim but with the following constraint: Suppose the previous player has just removed say


Algorithmica ◽  
2018 ◽  
Vol 82 (2) ◽  
pp. 212-244 ◽  
Author(s):  
Nathann Cohen ◽  
Fionn Mc Inerney ◽  
Nicolas Nisse ◽  
Stéphane Pérennes

1973 ◽  
Vol 14 (3) ◽  
pp. 298-301 ◽  
Author(s):  
P Erdös ◽  
J.L Selfridge
Keyword(s):  

2018 ◽  
Vol 47 (2) ◽  
pp. 375-377
Author(s):  
Aviezri Fraenkel ◽  
Urban Larsson ◽  
Carlos P. Santos ◽  
Bernhard von Stengel

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-34 ◽  
Author(s):  
Darius Bayegan ◽  
Megumi Harada

We develop the theory of poset pinball, a combinatorial game introduced by Harada-Tymoczko to study the equivariant cohomology ring of a GKM-compatible subspace X of a GKM space; Harada and Tymoczko also prove that, in certain circumstances, a successful outcome of Betti poset pinball yields a module basis for the equivariant cohomology ring of X. First we define the dimension pair algorithm, which yields a successful outcome of Betti poset pinball for any type A regular nilpotent Hessenberg and any type A nilpotent Springer variety, considered as GKM-compatible subspaces of the flag variety. The algorithm is motivated by a correspondence between Hessenberg affine cells and certain Schubert polynomials which we learned from Insko. Second, in a special case of regular nilpotent Hessenberg varieties, we prove that our pinball outcome is poset-upper-triangular, and hence the corresponding classes form a HS1*(pt)-module basis for the S1-equivariant cohomology ring of the Hessenberg variety.


2020 ◽  
Vol 68 ◽  
pp. 447-461
Author(s):  
Alexander Bradford ◽  
J. Kain Day ◽  
Laura Hutchinson ◽  
Bryan Kaperick ◽  
Craig Larson ◽  
...  

We demonstrate the use of a program that generates conjectures about positions of the combinatorial game Chomp—explanations of why certain moves are bad. These could be used in the design of a Chomp-playing program that gives reasons for its moves. We prove one of these Chomp conjectures—demonstrating that our conjecturing program can produce genuine Chomp knowledge. The conjectures are generated by a general purpose conjecturing program that was previously and successfully used to generate mathematical conjectures. Our program is initialized with Chomp invariants and example game boards—the conjectures take the form of invariant-relation statements interpreted to be true for all board positions of a certain kind. The conjectures describe a theory of Chomp positions. The program uses limited, natural input and suggests how theories generated on-the-fly might be used in a variety of situations where decisions—based on reasons—are required.


2020 ◽  
Vol 17 (2) ◽  
pp. 213-223
Author(s):  
Barbara Tomalak

Mythicising and Mythologising: On Dorota Siwor’s book, Traces of Myth and Ritual The author discusses the issues touched upon in the book penned by Dorota Siwor, Traces of Myth and Ritual. On Polish Contemporary Prose – Not Only the Latest such as myth, mythologising and mythicising the presented world in the analysed books. She presents them in the context of research theories concerning myth, also, analysing the interpretative conceptions proposed by Siwor. She emphasises the quality of the publication, author’s erudition and the freedom in the selection of threads and motifs, which create a multidimensional space for combinatorial game suggesting potential Fullness, Jung’s coniunctio oppositorum – the union of form and matter, the imagined and real-world, culture and nature. She also indicates the fields on which polemics and criticism of the selection of the theories applied are possible.


Author(s):  
Khaled Sliman Aloklah

  Game Theory is defined as a means of mathematical analysis when interests collide with each other to reach the best possible decision-making options taking into consideration the given circumstances to get the desired results. Even though Game Theory is related to well-known games such as checkers, XO, and poker. In fact, it is associated with more serious problems pertaining to sociology, economics, politics, military sciences. Game Theory includes several sorts of games like Combinatorial Games. This Paper gives the reader a detailed outlook of a special Combinatorial game called Nim Game. Before the start of the game we will develop a strategy to determine the winner in advance with the help of some basic mathematical concepts like Minimum Excluded (MEX), Grundy Numbers and The XOR Number.    


Sign in / Sign up

Export Citation Format

Share Document