On orbits of order ideals of minuscule posets

David B. Rush1, XiaoLin Danny Shi1
1Department of Mathematics [MIT]

Tóm tắt

Từ khóa


Tài liệu tham khảo

Andrews, G.E.: Plane partitions (II): the equivalence of the Bender–Knuth and MacMahon conjectures. Pac. J. Math. 72, 283–291 (1977)

Björner, A., Brenti, F.: Combinatorics of Coxeter Groups. Springer, New York (2005)

Brouwer, A., Schrijver, A.: On the period of an operator, defined on antichains. Math. Centrum Report ZW 24 (1974)

Cameron, P.J., Fon-Der-Flaass, D.G.: Orbits of antichains revisited. Eur. J. Comb. 16, 545–554 (1995)

Duchet, P.: Sur les hypergraphes invariants. Discrete Math. 8, 269–280 (1974)

Fon-Der-Flaass, D.G.: Orbits of antichains in ranked posets. Eur. J. Comb. 14, 17–22 (1993)

Guo, V.J.W., Zeng, J.: Some arithmetic properties of the q-Euler numbers and q-Salié numbers. Eur. J. Comb. 27, 884–895 (2006)

Proctor, R.A.: Bruhat lattices, plane partition generating functions, and minuscule representations. Eur. J. Comb. 5, 331–350 (1984)

Reiner, V., Stanton, D., White, D.: The cyclic sieving phenomenon. J. Comb. Theory, Ser. A 108, 17–50 (2004)

Rush, D.B., Shi, X.: On orbits of order ideals of minuscule posets. REU report, www.math.umn.edu/~reiner/REU/RushShi2011.pdf (2011)

Springer, T.A.: Regular elements of finite reflection groups. Invent. Math. 25, 159–198 (1974)

Stanley, R.P.: Enumerative Combinatorics: Vol. I. Cambridge University Press, New York (1997)

Stanley, R.P.: Promotion and evacuation. Electron. J. Comb. 16, R9 (2009)

Stembridge, J.R.: On minuscule representations, plane partitions and involutions in complex Lie groups. Duke Math. J. 73, 469–490 (1994)

Stembridge, J.R.: On the fully commutative elements of Coxeter groups. J. Algebr. Comb. 5, 353–385 (1996)

Striker, J., Williams, N.: Promotion and Rowmotion (2011). arXiv: 1108.1172v1 [math.CO]

Wildberger, N.J.: Minuscule posets from neighbourly graph sequences. Eur. J. Comb. 24, 741–757 (2003)