125 research outputs found
New interpretations for noncrossing partitions of classical types
We interpret noncrossing partitions of type and type in terms of
noncrossing partitions of type . As an application, we get type-preserving
bijections between noncrossing and nonnesting partitions of type , type
and type which are different from those in the recent work of Fink and
Giraldo. We also define Catalan tableaux of type and type , and find
bijections between them and noncrossing partitions of type and type
respectively.Comment: 21 pages, 15 figures, final versio
Chain enumeration of -divisible noncrossing partitions of classical types
We give combinatorial proofs of the formulas for the number of multichains in
the -divisible noncrossing partitions of classical types with certain
conditions on the rank and the block size due to Krattenthaler and M{\"u}ller.
We also prove Armstrong's conjecture on the zeta polynomial of the poset of
-divisible noncrossing partitions of type invariant under a
rotation in the cyclic representation.Comment: 23 pages, 9 figures, final versio
Promotion and Rowmotion
We present an equivariant bijection between two actions--promotion and
rowmotion--on order ideals in certain posets. This bijection simultaneously
generalizes a result of R. Stanley concerning promotion on the linear
extensions of two disjoint chains and recent work of D. Armstrong, C. Stump,
and H. Thomas on root posets and noncrossing partitions. We apply this
bijection to several classes of posets, obtaining equivariant bijections to
various known objects under rotation. We extend the same idea to give an
equivariant bijection between alternating sign matrices under rowmotion and
under B. Wieland's gyration. Finally, we define two actions with related orders
on alternating sign matrices and totally symmetric self-complementary plane
partitions.Comment: 25 pages, 22 figures; final versio
Relations between cumulants in noncommutative probability
We express classical, free, Boolean and monotone cumulants in terms of each
other, using combinatorics of heaps, pyramids, Tutte polynomials and
permutations. We completely determine the coefficients of these formulas with
the exception of the formula for classical cumulants in terms of monotone
cumulants whose coefficients are only partially computed.Comment: 27 pages, 7 figures, AMS LaTe
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