
Matroid maps
| Категория реферата: Топики по английскому языку
| Теги реферата: банк курсовых, дипломная работа образец
| Добавил(а) на сайт: Semenovskij.
Предыдущая страница реферата | 1 2
Доказательство. If is a matroid map then the
satisfaction of conditions (1) and (2) is the main result of [2].
Assume now that satisfies the conditions (1) and
(2).
First we introduce, for any two
adjacent fibbers and
of the map
, the wall
separating them. Let
be the set of all walls
.
Now take two arbitrary residues and chambers
and
. We wish to prove
.
Consider a geodesic gallery
connecting the chambers u and v. Let
now the chamber x moves along from u to v, then the corresponding
residue
moves from
to
. Since the geodesic gallery
intersects every wall no more than
once [5, Lemma 2.5], the chamber x crosses each wall
in
no more than once and, if it crosses
, it moves from the same side of
as u to the opposite side. But, by
the assumptions of the theorem, this means that the residue
crosses each wall
no more than once and moves from the
side of
opposite u to the side containing u.
But, by the geometric interpretation of the Bruhat order, this means [2, Theorem 5.7] that
decreases, with respect to the
u-Bruhat order, at every such step, and we ultimately obtain
Список литературы
Borovik A.V., Gelfand I.M. WP-matroids and thin Schubert cells on Tits systems // Advances Math. 1994. V.103. N.1. P.162-179.
Borovik A.V., Roberts K.S. Coxeter groups and matroids, in Groups of Lie Type and Geometries, W. M. Kantor and L. Di Martino, eds. Cambridge University Press. Cambridge, 1995 (London Math. Soc. Lect. Notes Ser. V.207) P.13-34.
Gale D., Optimal assignments in an ordered set: an application of matroid theory // J. Combinatorial Theory. 1968. V.4. P.1073-1082.
Gelfand I.M., Serganova V.V. Combinatorial geometries and torus strata on homogeneous compact manifolds // Russian Math. Surveys. 1987. V.42. P.133-168.
Ronan M. Lectures on Buildings - Academic Press. Boston. 1989.
Tits J. A local approach to buildings, in The Geometric Vein (Coxeter Festschrift) Springer-Verlag, New York a.o., 1981. P.317-322.
Скачали данный реферат: Клариса, Галактион, Evangelina, Kajnazarov, Jafaev, Махнёв, Агабабян, Копейкин.
Последние просмотренные рефераты на тему: реферат на тему время, загадки с ответами, шпаргалки по менеджменту, мини сочинение.
Категории:
Предыдущая страница реферата | 1 2