198 research outputs found
Record-dependent measures on the symmetric groups
A probability measure P[subscript n] on the symmetric group S[subscript n] is said to be record-dependent if P[subscript n]( σ ) depends only on the set of records of a permutation σ ∈ S[subscript n]. A sequence P = ( P n )[subscript n ∈ N] of consistent record-dependent measures determines a random order on N. In this paper we describe the extreme elements of the convex set of such P. This problem turns out to be related to the study of asymptotic behavior of permutation-valued growth processes, to random extensions of partial orders, and to the measures on the Young-Fibonacci lattice
Block characters of the symmetric groups
A block character of a finite symmetric group is a positive definite function which depends only on the number of cycles in a permutation. We describe the cone of block characters by identifying its extreme rays, and find relations of the characters to descent representations and the coinvariant algebra of S[subscript n]. The decomposition of extreme block characters into the sum of characters of irreducible representations gives rise to certain limit shape theorems for random Young diagrams. We also study counterparts of the block characters for the infinite symmetric group S[subscript n], along with their connection to the Thoma characters of the infinite linear group GL[subscript ∞](q) over a Galois field
Minimum and Complete Fluidization Velocity for Sand/Palm Shell Binary Mixtures, Part I: Fluidization Behaviour and Characteristic Velocities
Minimum and Complete Fluidization Velocity for Sand/Palm Shell Binary Mixtures, Part II: Characteristic Velocity Profiles, Critical Loading and Binary Correlations
A pattern theorem for random sorting networks
A sorting network is a shortest path from 12..n to n..21 in the Cayley graph
of the symmetric group S(n) generated by nearest-neighbor swaps. A pattern is a
sequence of swaps that forms an initial segment of some sorting network. We
prove that in a uniformly random n-element sorting network, any fixed pattern
occurs in at least cn^2 disjoint space-time locations, with probability tending
to 1 exponentially fast as n tends to infinity. Here c is a positive constant
which depends on the choice of pattern. As a consequence, the probability that
the uniformly random sorting network is geometrically realizable tends to 0.Comment: 21 pages, 9 figures. Final journal versio
Effect of particle and bed diameter on characteristic velocities in compartmented fluidized bed gasifier
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