Open AccessFIXED POINTS AND NEGATIVE CIRCUIT FREE IN FINITE LATTICES
Author(s) -
Juei-Ling Ho,
ShuHan Wu
Publication year - 2015
Publication title -
taiwanese journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.529
H-Index - 46
eISSN - 2224-6851
pISSN - 1027-5487
DOI - 10.11650/tjm.19.2015.3858
Subject(s) - mathematics , distributive property , lattice (music) , fixed point , graph , element (criminal law) , complete lattice , finite element method , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , universality (dynamical systems) , condensed matter physics , physics , law , political science , acoustics , thermodynamics
Let $X$ be a dimensional finite lattice (not necessary distributive) and let $F$ be a mapping from $X$ to $X$. Here we introduce a new notion of neighbours of an element of $X$ and prove that if all the neighbours of each element of $X$ are in $X$ and there is no negative circuit in the interaction graph of $F$, then $F$ has a fixed point.
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