Weyl groups, the hard Lefschetz theorem, and the Sperner property.(English)Zbl 0502.05004
MathOverflow Questions:
Important combinatorial and algebraic interpretations of the coefficients in the polynomial \([n]!_q = (1+q)(1+q+q^2) \ldots (1+q+\cdots + q^{n-1})\)Reference request: number of antichains of a partially ordered set
MSC:
| 05A05 | Permutations, words, matrices |
| 05A15 | Exact enumeration problems, generating functions |
| 14L35 | Classical groups (algebro-geometric aspects) |
| 06A06 | Partial orders, general |
| 20G20 | Linear algebraic groups over the reals, the complexes, the quaternions |
Keywords:
hard Lefschetz theorem;finite partially ordered sets;algebraic varieties;k-Sperner property;complex semisimple algebraic group;parabolic subgroup;Bruhat order;Weyl groupCite
Full Text:DOI
Online Encyclopedia of Integer Sequences:
Constant term in expansion of (1/2) * Product_{k=-n..n} (1 + x^k).The size of the largest antichain in the 7-dimensional hypercubic lattice of size n; also the coefficient of x^floor(7*(n-1)/2) in (1 + x + ... + x^(n-1))^7.
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