Permutation statistics related to a class of noncommutative symmetric functions and generalizations of the Genocchi numbers [PDF]
, 2007 .We prove conjectures of the third author [L. Tevlin, Proc. FPSAC’07, Tianjin] on two new bases of noncommutative symmetric functions: the transition matrices from the ribbon basis have nonnegative integral coefficients.
F. Hivert +3 more
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On words of non-Hermitian random matrices [PDF]
Annals of Probability, 2019 We consider words $G_{i_1} \cdots G_{i_m}$ involving i.i.d. complex Ginibre matrices, and study their singular values and eigenvalues. We show that the limit distribution of the squared singular values of every word of length $m$ is a Fuss-Catalan ...
Guillaume Dubach, Y. Peled
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The Energy Operator for a Model with a Multiparametric Infinite Statistics [PDF]
, 2003 In this paper we consider energy operator (a free Hamiltonian), in the second-quantized approach, for the multiparameter quon algebras: $a_{i}a_{j}^{\dagger}-q_{ij}a_{j}^{\dagger}a_{i} = \delta_{ij}, i,j\in I$ with $(q_{ij})_{i,j\in I}$ any hermitian ...
Ante Perica +13 more
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Towards Optimal Estimation of Bivariate Isotonic Matrices with Unknown Permutations [PDF]
Annals of Statistics, 2018 Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns.
Cheng Mao, A. Pananjady, M. Wainwright
semanticscholar +1 more source
Refining the bijections among ascent sequences, (2+2)-free posets, integer matrices and pattern-avoiding permutations [PDF]
Journal of Combinatorial Theory, 2018 The combined work of Bousquet-M\'elou, Claesson, Dukes, Jel\'inek, Kitaev, Kubitzke and Parviainen has resulted in non-trivial bijections among ascent sequences, (2+2)-free posets, upper-triangular integer matrices, and pattern-avoiding permutations.
M. Dukes, Peter R. W. McNamara
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Proof of a Symmetrized Trace Conjecture for the Abelian Born-Infeld Lagrangian [PDF]
, 2000 In this paper we prove a conjecture regarding the form of the Born-Infeld Lagrangian with a U(1)^2n gauge group after the elimination of the auxiliary fields.
Aschieri +8 more
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Equidistributed Statistics on Fishburn Matrices and Permutations [PDF]
Electronic Journal of Combinatorics, 2018 Recently, Jelinek conjectured that there exists a bijection between certain restricted permutations and Fishburn matrices such that the bijection verifies the equidistribution of several statistics. The main objective of this paper is to establish such a
Dandan Chen +2 more
semanticscholar +1 more source
Complex Analysis and Operator Theory, 2023 Quantum permutations arise in many aspects of modern “quantum mathematics”. However, the aim of this article is to detach these objects from their context and to give a friendly introduction purely within operator theory.
Moritz Weber
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The Matrix Ansatz, Orthogonal Polynomials, and Permutations [PDF]
, 2010 In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We illustrate this
Corteel, Sylvie +2 more
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On the joint distribution of the marginals of multipartite random quantum states [PDF]
, 2020 We study the joint distribution of the set of all marginals of a random Wishart matrix acting on a tensor product Hilbert space. We compute the limiting free mixed cumulants of the marginals, and we show that in the balanced asymptotical regime, the ...
Dartois, Stephane +2 more
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