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ORTHOGONAL SYMMETRIC CHAIN DECOMPOSITIONS OF HYPERCUBES\ast
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kdagger, Hunter S. P. I. N. |
| Copyright Year | 2019 |
| Abstract | In 1979, Shearer and Kleitman conjectured the existence of \lfloor n/2\rfloor +1 orthogonal chain decompositions of the hypercube poset Qn and constructed two orthogonal chain decompositions. In this paper, we make the first nontrivial progress on this conjecture by constructing three orthogonal chain decompositions of Qn for all n \geq 4 with the possible exceptions n = 9, 11, 13, 23. To do this, we introduce the notion of ``almost orthogonal symmetric chain decompositions."" We explicitly describe three such decompositions of Q5 and Q7 and describe conditions which allow us to decompose products of hypercube posets into k almost orthogonal symmetric chain decompositions given such decompositions of the original hypercube posets. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.harvard.edu/~hspink/Orthogonal.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
