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- W2577855391 abstract "In [4], B. Kim, and the authors classified 2-chains with 1-shell boundaries into either RN (renamable)-type or NR (non renamable)-type 2-chains up to renamability of support of subsummands of a 2-chain and introduced the notion of chain-walk, which was motivated from graph theory: a directed walk in a directed graph is a sequence of edges with compatible condition on initial and terminal vertices between sequential edges. We consider a directed graph whose vertices are 1-simplices whose supports contain $0$ and edges are plus/minus of $2$-simplices whose supports contain $0$. A chain-walk is a 2-chain induced from a directed walk in this graph. We reduced any 2-chains with 1-shell boundaries into chain-walks having the same boundaries. In this paper, we reduce any 2-chains of 1-shell boundaries into chain-walks of the same boundary with support of size $3$. Using this reduction, we give a combinatorial criterion determining whether a minimal 2-chain is of RN- or NR-type. For a minimal RN-type 2-chains, we show that it is equivalent to a 2-chain of Lascar type (coming from model theory) if and only if it is equivalent to a planar type 2-chain." @default.
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- W2577855391 date "2017-01-01" @default.
- W2577855391 modified "2023-09-29" @default.
- W2577855391 title "More on 2-chains with 1-shell boundaries in rosy theories" @default.
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- W2577855391 doi "https://doi.org/10.2969/jmsj/06910093" @default.
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