6,237 research outputs found
FPRAS for computing a lower bound for weighted matching polynomial of graphs
We give a fully polynomial randomized approximation scheme to compute a lower
bound for the matching polynomial of any weighted graph at a positive argument.
For the matching polynomial of complete bipartite graphs with bounded weights
these lower bounds are asymptotically optimal.Comment: 16 page
Equality in Wielandt's eigenvalue inequality
In this paper we give necessary and sufficient conditions for the equality
case in Wielandt's eigenvalue inequality.Comment: 6 pages, few typos are correcte
Nonnegative definite hermitian matrices with increasing principal minors
A nonzero nonnegative definite hermitian m by m matrix A has increasing
principal minors if the value of each principle minor of A is not less than the
value each of its subminors. For we show has increasing principal
minors if and only if exists and its diagonal entries are less or
equal to 1.Comment: 3 page
On crystal operators in Lusztig's parametrizations and string cone defining inequalities
Let be a reduced expression for the longest element of the
Weyl group, adapted to a quiver of type . We compare Lusztig's and
Kashiwara's (string) parametrizations of the canonical basis associated with
. Crystal operators act in a finite number of patterns in
Lusztig's parametrization, which may be seen as vectors. We show this set gives
the system of defining inequalities of the string cone constructed by Gleizer
and Postnikov. We use combinatorics of Auslander-Reiten quivers, and as a
by-product we get an alternative enumeration of a set of inequalities defining
the string cone, based on hammocks.Comment: To appear in Glasgow Mathematical Journal. Revised version of LMNO
preprint 2011-23 UMR CNRS 6139, Caen University, Franc
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