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Dyck Paths, Binary Words, and Grassmannian Permutations Avoiding an Increasing Pattern
Annals of Combinatorics, 2022A permutation is called Grassmannian if it has at most one descent. The study of pattern avoidance in such permutations was initiated by Gil and Tomasko in 2021. We continue this work by studying Grassmannian permutations that avoid an increasing pattern.
Krishna Menon, Anurag Singh
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Annular noncrossing permutations and partitions, and second-order asymptotics for random matrices
, 2003We study the set Sann−nc(p,q) of permutations of {1, …, p+q} which are noncrossing in an annulus with p points marked on its external circle and q points marked on its internal circle.
J. Mingo, A. Nica
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Generalized De Bruijn Words, Invertible Necklaces, and the Burrows-Wheeler Transform
International Symposium on Mathematical Foundations of Computer ScienceWe define generalized de Bruijn words as those words having a Burrows-Wheeler transform that is a concatenation of permutations of the alphabet. We show that generalized de Bruijn words are in 1-to-1 correspondence with Hamiltonian cycles in the ...
Gabriele Fici, Estéban Gabory
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Efficient Unitary Designs from Random Sums and Permutations
IEEE Annual Symposium on Foundations of Computer ScienceA unitary k-design is an ensemble of unitaries that matches the first $k$ moments of the Haar measure. In this work, we provide two efficient constructions of k-designs on n-qubits using new random matrix theory techniques.
Chi-Fang Chen +5 more
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Block Encoding of Sparse Matrices via Coherent Permutation
arXiv.orgBlock encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices remains a ...
Abhishek Setty
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On Rotation Group and Encryption of Analog Signals
Annual International Cryptology Conference, 1985Su-shing Chen
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