2,250 research outputs found
An affine generalization of evacuation
We establish the existence of an involution on tabloids that is analogous to
Schutzenberger's evacuation map on standard Young tableaux. We find that the
number of its fixed points is given by evaluating a certain Green's polynomial
at , and satisfies a "domino-like" recurrence relation.Comment: 32 pages, 7 figure
Decomposing labeled interval orders as pairs of permutations
We introduce ballot matrices, a signed combinatorial structure whose
definition naturally follows from the generating function for labeled interval
orders. A sign reversing involution on ballot matrices is defined. We show that
matrices fixed under this involution are in bijection with labeled interval
orders and that they decompose to a pair consisting of a permutation and an
inversion table. To fully classify such pairs, results pertaining to the
enumeration of permutations having a given set of ascent bottoms are given.
This allows for a new formula for the number of labeled interval orders
Real K3 surfaces with non-symplectic involution and applications. II
We consider real forms of relatively minimal rational surfaces F_m. Connected
components of moduli of real non-singular curves in |-2K_{F_m}| had been
classified recently for m=0, 1, 4 in math.AG/0312396. Applying similar methods,
here we fill the gap for m=2 and m=3 to complete similar classification for any
0\le m\le 4 when |-2K_{F_m}| is reduced.
The case of F_2 is especially remarkable and classical (quadratic cone in
P^3). As an application, we finished classification of connected components of
moduli of real hyper-elliptically polarized K3 surfaces and their deformations
to real polarized K3 surfaces started in math.AG/0312396, math.AG/0507197. This
could be important in some questions because real hyper-elliptically polarized
K3 surfaces can be constructed explicitly.Comment: 22 pages, 6 figure
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