Values
=>
Cc0014;cc-rep
([],1)=>0
([],2)=>0
([(0,1)],2)=>0
([],3)=>0
([(0,1),(0,2)],3)=>0
([(0,2),(2,1)],3)=>0
([(0,2),(1,2)],3)=>0
([],4)=>0
([(0,1),(0,2),(0,3)],4)=>1
([(0,2),(0,3),(3,1)],4)=>0
([(0,1),(0,2),(1,3),(2,3)],4)=>0
([(1,2),(2,3)],4)=>0
([(0,3),(3,1),(3,2)],4)=>1
([(1,3),(2,3)],4)=>0
([(0,3),(1,3),(3,2)],4)=>1
([(0,3),(1,3),(2,3)],4)=>1
([(0,3),(1,2),(1,3)],4)=>0
([(0,2),(0,3),(1,2),(1,3)],4)=>2
([(0,3),(2,1),(3,2)],4)=>0
([(0,3),(1,2),(2,3)],4)=>0
([],5)=>0
([(0,1),(0,2),(0,3),(0,4)],5)=>2
([(0,2),(0,3),(0,4),(4,1)],5)=>1
([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>1
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(4,1),(4,2)],5)=>1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>1
([(0,3),(0,4),(3,2),(4,1)],5)=>0
([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>2
([(2,3),(3,4)],5)=>0
([(0,4),(4,1),(4,2),(4,3)],5)=>2
([(2,4),(3,4)],5)=>0
([(1,4),(2,4),(4,3)],5)=>1
([(0,4),(1,4),(4,2),(4,3)],5)=>2
([(0,4),(1,4),(2,4),(4,3)],5)=>2
([(0,4),(1,4),(2,4),(3,4)],5)=>2
([(0,4),(1,4),(2,3)],5)=>0
([(0,4),(1,3),(2,3),(2,4)],5)=>0
([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>3
([(0,4),(1,4),(2,3),(4,2)],5)=>1
([(0,4),(1,3),(2,3),(3,4)],5)=>1
([(0,4),(1,4),(2,3),(2,4)],5)=>1
([(0,4),(1,4),(2,3),(3,4)],5)=>1
([(0,4),(1,2),(1,4),(2,3)],5)=>0
([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>2
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>2
([(0,4),(1,2),(1,4),(4,3)],5)=>1
([(0,4),(1,2),(1,3),(1,4)],5)=>1
([(0,2),(0,4),(3,1),(4,3)],5)=>0
([(0,4),(1,2),(1,3),(3,4)],5)=>0
([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(1,2),(1,4)],5)=>0
([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>3
([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>2
([(0,3),(1,2),(1,4),(3,4)],5)=>0
([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>2
([(1,4),(3,2),(4,3)],5)=>0
([(0,3),(3,4),(4,1),(4,2)],5)=>1
([(1,4),(2,3),(3,4)],5)=>0
([(0,4),(1,2),(2,4),(4,3)],5)=>1
([(0,3),(1,4),(4,2)],5)=>0
([(0,4),(3,2),(4,1),(4,3)],5)=>1
([(0,4),(1,2),(2,3),(2,4)],5)=>1
([(0,4),(2,3),(3,1),(4,2)],5)=>0
([(0,3),(1,2),(2,4),(3,4)],5)=>0
([(0,4),(1,2),(2,3),(3,4)],5)=>0
([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>1
([],6)=>0
([(3,4),(4,5)],6)=>0
([(2,3),(3,5),(5,4)],6)=>0
([(3,5),(4,5)],6)=>0
([(2,5),(3,5),(5,4)],6)=>1
([(0,5),(1,5),(2,5),(3,5),(5,4)],6)=>3
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>2
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>2
([(1,5),(2,5),(3,4)],6)=>0
([(1,5),(2,4),(3,4),(3,5)],6)=>0
([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)=>2
([(1,5),(2,5),(3,4),(5,3)],6)=>1
([(1,5),(2,4),(3,4),(4,5)],6)=>1
([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>2
([(0,5),(1,5),(2,3),(5,4)],6)=>1
([(1,5),(2,5),(3,4),(4,5)],6)=>1
([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>2
([(0,5),(1,5),(2,3),(3,4)],6)=>0
([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>1
([(0,4),(1,4),(2,3),(3,5),(4,5)],6)=>1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1
([(0,5),(1,5),(2,4),(3,4)],6)=>0
([(0,5),(1,4),(2,4),(3,5),(4,3)],6)=>1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>2
([(2,5),(3,4),(4,5)],6)=>0
([(1,5),(2,3),(3,5),(5,4)],6)=>1
([(1,3),(2,4),(4,5)],6)=>0
([(1,5),(3,4),(4,2),(5,3)],6)=>0
([(1,4),(2,3),(3,5),(4,5)],6)=>0
([(0,4),(1,3),(3,5),(4,5),(5,2)],6)=>1
([(0,5),(1,4),(4,2),(5,3)],6)=>0
([(1,5),(2,3),(3,4),(4,5)],6)=>0
([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>1
([(0,4),(1,4),(1,5),(2,3),(3,5)],6)=>0
([(0,5),(1,3),(4,2),(5,4)],6)=>0
([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>0
([(0,5),(1,3),(2,4),(4,5)],6)=>0
([(0,5),(1,4),(2,3),(3,4),(3,5)],6)=>1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>1
([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>1
([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>0
([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>1
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Description
The interval resolution global dimension of a poset.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
This is the cardinality of the longest chain of right minimal approximations by interval modules of an indecomposable module over the incidence algebra.
References
[1] Aoki, T., Escolar, E. G., Tada, S. Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions arXiv:2308.14979
[2] https://github.com/xHoukakun/Interval-Resolution-Global-Dimension/tree/main
[2] https://github.com/xHoukakun/Interval-Resolution-Global-Dimension/tree/main
Created
Mar 07, 2025 at 13:26 by Jannek Müller
Updated
Mar 07, 2025 at 15:43 by Jannek Müller
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