2022/06/05 by Ghouchan, Mohammad Farrokhi Derakhshandeh
#05C99 (Secondary) #52B11 #52B15 (Primary) 52B05 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2206.03323
We generalize Venn diagrams in spaces of arbitrary dimension ≥ 2 and study simple Venn diagrams with the reducing property. Three equivalent conditions for a simple Venn diagram to reduce it completely and a classification of those diagrams is discussed. For example, we show that a simple m-dimensional n-Venn diagram is fully reducible if n≤ m+1 and conjecture that the converse is also true. An application of the generalized Venn diagrams and some more open problems are given.