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1
Symmetric Functions, Schubert Polynomials, and Degeneracy Loci
Describe these permutations completely.3 Dominant permutations and
bigrassmannian permutations are special cases of a larger class of permutations,
called vexillary.4 DEFINITION 2.2.6. A permutation is called vexillary if its
diagram, up to ...
2
Surveys in Combinatorics, 1991
(iv) A(w)' = \(w~i). A permutation w G 5^ is said to be vexillary if it satisfies these
equivalent conditions. By (1.5) (iii), the first non- vexillary permutation is (2143) in
S4. Amongst the vexillary permutations, there are two particular subclasses: (i) ...
3
The Natural History of Plants
Still, generally speaking, the embryo is straight,7 and the imbrication of the
corolla is not vexillary. But there are several members of the series Bauhiniea in
which the radicle is curved, and on the other hand in many Papilionacea the
radicle is ...
4
Singular Loci of Schubert Varieties
Lascoux [114] has extended this algorithm to the set of vexillary permutations.
Boe [17] has generalized the above results to all Hermitian symmetric spaces
while keeping the same flavor of the algorithm. In an effort to find a geometric
proof of ...
Sara Billey, V. Lakshmibai, 2000
5
K-schur Functions and Affine Schubert Calculus
1.7). Show that EdelmanGreene insertion ofi∈R(w) is the usual Robinson
Schensted insertion of i. (Vexillary permutations [19]) A permutationw∈ S n is
vexillary ifit avoids thepattern2143.That is,there do not exista< b < c<d such thatw
(b)<w(a) ...
6
Symmetric Functions and Combinatorial Operators on Polynomials
1.34 134. In the case of a vexillary permutation cr, there is only one tableau which
is a reduced decomposition of cr, and the two above packings produce the same
tableau. The smallest example of a non- vexillary permutation is a = [2,1, 4, 3].
7
Enumerative Combinatorics:
vertex final, 500 initial, 500 of a graph, see graph, vertex of a polytope, see
polytope, convex, vertex very pure, see monoid, very pure vexillary permutation,
see permutation, vexillary Viennot, X. G. boustrephedon triangle, 175 difference
tables, ...
8
Patterns in Permutations and Words
... 39, 228–230, 241, 248, 249, 339, 340, 342 Vershik, A. M., 242 vertical
alternation, 320 vexillary involution, 266 vexillary involutions fixed under the
composition of reverse and complement, 267 vexillary permutation, 256, 399
Viennot, X. G., ...
9
Centrosema: Biology, Agronomy, and Utilization
Calyx teeth almost obsolete, dorsal and lateral teeth reduced to a shallow convex
lobe; vexillary spur present; stipules triangular to lanceolate, prominent but
separate; stems coarse, angular but not thickened or winged at corners 31 31a.
Rainer Schultze-Kraft, R. J. Clements, 1990
10
Flora Capensis: Being a Systematic Description of the Plants ...
Ake oblong, Bimple, short- clawed. Carina straightish, slightly longer than the
vexillum. Vexillary stamen slightly adnate in the middle. Style compressed and
flattish below, subterete and villous toward the inflexed point. Calyx strumose at
base.
William Henry Harvey, O. W. Sonder, 1862
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Bright beds of jubilation
To be sure of the right layout, Suttons can supply a biodegradable Union flag template, through which the seedlings will grow, to form a living vexillary bed in ... «Telegraph.co.uk, 3월 12»
