The Automorphism Group of the Fibonacci Poset: A “Not Too Difficult” Problem of Stanley from 1988
Jonathan David Farley
and Sungsoon Kim
Department of Applied Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
DOI: 10.1023/B:JACO.0000023007.96063.b3
Abstract
All of the automorphisms of the Fibonacci poset Z( r) are determined ( r \mathbb N \mathbb{N} ). A problem of Richard P. Stanley from 1988 is thereby solved.
Pages: 197–204
Keywords: Fibonacci poset; Fibonacci lattice; differential poset; automorphism group; $(partially)$ ordered set
Full Text: PDF
References
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2. B.A. Davey and H.A. Priestly, Introduction to Lattices and Order, 2nd edition, Cambridge University Press, Cambridge, 2002.
3. F.M. Goodman and S.V. Kerov, “The Martin boundary of the Young-Fibonacci lattice,” Journal of Algebraic Combinatorics 11 (2000), 17-48.
4. R. Kemp, “Tableaux and rank-selection in Fibonacci lattices,” European Journal of Combinatorics 18 (1997), 179-193.
5. D. Kremer, “A bijection between intervals in the Fibonacci posets,” Discrete Mathematics 217 (2000), 225- 235.
6. D. Kremer and K.M. O'Hara, “A bijection between maximal chains in Fibonacci posets,” Journal of Combinatorial Theory (A) 78 (1997), 268-279.
7. S. Okada, “Algebras associated to the Young-Fibonacci lattice,” Transactions of the American Mathematical Society 346 (1994), 549-568.
8. R.P. Stanley, “The Fibonacci lattice,” The Fibonacci Quartely 13 (1975), 215-232.
9. R.P. Stanley, “Differential posets,” Journal of the American Mathematical Society 1 (1988), 919-961.
10. R.P. Stanley, “Further combinatorial properties of two Fibonacci lattices,” European Journal of Combinatorics 11 (1990), 181-188.