6 research outputs found
Young tableau reconstruction via minors
The tableau reconstruction problem, posed by Monks (2009), asks the
following. Starting with a standard Young tableau , a 1-minor of is a
tableau obtained by first deleting any cell of , and then performing jeu de
taquin slides to fill the resulting gap. This can be iterated to arrive at the
set of -minors of . The problem is this: given , what are the values
of such that every tableau of size can be reconstructed from its set of
-minors? For , the problem was recently solved by Cain and Lehtonen. In
this paper, we solve the problem for , proving the sharp lower bound . In the case of multisets of -minors, we also give a lower bound for
arbitrary , as a first step toward a sharp bound in the general multiset
case.Comment: 24 pages, 18 figure
On the -hull number and infecting times of generalized Petersen graphs
The -hull number of a graph is the minimum cardinality of an infecting
set of vertices that will eventually infect the entire graph under the rule
that uninfected nodes become infected if two or more neighbors are infected. In
this paper, we study the -hull number for generalized Petersen graphs and
a number of closely related graphs that arise from surgery or more generalized
permutations. In addition, the number of components of the complement of an
infecting set of minimum cardinality is calculated for the generalized Petersen
graph and shown to always be or . Moreover, infecting times for
infecting sets of minimum cardinality are studied. Bounds are provided and
complete information is given in special cases.Comment: 8 page