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- W2185691387 abstract "With the term 'anti-monotonic function', we designate spe- cific boolean functions on subsets of a finite set of positive integers which we call the universe. Through the well-known bijective relationship be- tween the set of monotonic functions and the set of anti-monotonic func- tions, the study of the anti-monotonic functions is equivalent to the study of monotonic functions. The true-set of an anti-monotonic function is an antichain. If the universe is denoted by N, the set of anti-monotonic functions is denoted by AMF (N). This set can be partially ordered in a natural way. This paper studies enumeration in the resulting lattice of anti-monotonic functions. We define intervals of anti-monotonic func- tions according to this order and present four properties of such intervals, Finally we give a formula for the size of a general interval and a recursion formula for the n-th number of Dedekind." @default.
- W2185691387 created "2016-06-24" @default.
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- W2185691387 date "2013-10-11" @default.
- W2185691387 modified "2023-09-23" @default.
- W2185691387 title "Decomposition of Intervals in the Space of Anti-Monotonic Functions" @default.
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