Brouwer's theorem for a square on the basis of Hex theorem

• Autorzy: Barcz, Eugeniusz
• Języki publikacji: EN

Abstrakty

EN

This work is a continuation of author's work [1] on fixed points. In this work, Brouwer's theorem is proved on the basis of the Hex theorem. In the proof, the author uses, among other things, the lemma about no draw. Two proofs of this lemma are derived. The second proof is a modification of D. Gale's proof [2] and is based on the concept of a walk on the Hex board.

Słowa kluczowe

PL

gra Hex; podwójna plansza; graf planarny; lemat Spernera; twierdzenie Brouwera

EN

game of Hex; dual board; planar graph; Sperner's lemma; Brouwer's theorem

• Czasopismo: Silesian Journal of Pure and Applied Mathematics
• Rocznik: 2022
• Tom: Vol. 12, iss. 1
• Strony: 33--44
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Barcz, Eugeniusz

• University of Warmia and Mazury, Faculty of Mathematics and Computer Science, Chair of Complex Analysis, Słoneczna 54 Street, 10-710 Olsztyn, Poland,

Bibliografia

• 1. Barcz E.:A new Proof and Consequences of the Fixed Point Theorem of Matkowski. Annales Mathematicae Silesianae 35, no. 2, 149-157, 2021.
• 2. Gale D.: The game of Hex and the Brouwer Fixed-Point Theorem. The American Mathematical Monthly, Vol. 86, No. 10, 818-827.
• 3. Szulc J.: Lemat Spernera, czyli co wspólnego mają trójkąty i sprawiedliwy podział Delta nr 3, 2020.