6,439 research outputs found
Order Quasisymmetric Functions Distinguish Rooted Trees
Richard P. Stanley conjectured that finite trees can be distinguished by
their chromatic symmetric functions. In this paper, we prove an analogous
statement for posets: Finite rooted trees can be distinguished by their order
quasisymmetric functions.Comment: 16 pages, 5 figures, referees' suggestions incorporate
Algebraic structures on graph cohomology
We define algebraic structures on graph cohomology and prove that they
correspond to algebraic structures on the cohomology of the spaces of
imbeddings of S^1 or R into R^n. As a corollary, we deduce the existence of an
infinite number of nontrivial cohomology classes in Imb(S^1,R^n) when n is even
and greater than 3. Finally, we give a new interpretation of the anomaly term
for the Vassiliev invariants in R^3.Comment: Typos corrected, exposition improved. 14 pages, 2 figures. To appear
in J. Knot Theory Ramification
Generalization of Schensted insertion algorithm to the cases of hooks and semi-shuffles
Given an rc-graph of permutation and an rc-graph of permutation
, we provide an insertion algorithm, which defines an rc-graph in the case when is a shuffle with the descent at and has no
descents greater than or in the case when is a shuffle, whose shape is
a hook. This algorithm gives a combinatorial rule for computing the generalized
Littlewood-Richardson coefficients in the two cases mentioned
above.Comment: 22 page
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