33,293 research outputs found
Role of initial conditions in the Universe formation
A dependence of low energy physics on initial conditions in the framework of
multidimensional gravity is discussed. It is shown that the observable
symmetries could be a result of specific topologies originated from space-time
foam.Comment: 20 page
Snow Leopard Permutations and Their Even and Odd Threads
Caffrey, Egge, Michel, Rubin and Ver Steegh recently introduced snow leopard
permutations, which are the anti-Baxter permutations that are compatible with
the doubly alternating Baxter permutations. Among other things, they showed
that these permutations preserve parity, and that the number of snow leopard
permutations of length is the Catalan number . In this paper we
investigate the permutations that the snow leopard permutations induce on their
even and odd entries; we call these the even threads and the odd threads,
respectively. We give recursive bijections between these permutations and
certain families of Catalan paths. We characterize the odd (resp. even) threads
which form the other half of a snow leopard permutation whose even (resp. odd)
thread is layered in terms of pattern avoidance, and we give a constructive
bijection between the set of permutations of length which are both even
threads and odd threads and the set of peakless Motzkin paths of length .Comment: 25 pages, 6 figures. Version 3 is modified to use standard Discrete
Mathematics and Theoretical Computer Science but is otherwise unchange
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