相关论文: Permutation Invariant Statistics, Duality and Simp…

Many matching, tracking, sorting, and ranking problems require probabilistic reasoning about possible permutations, a set that grows factorially with dimension. Combinatorial optimization algorithms may enable efficient point estimation,…

We prove several general formulas for the distributions of various permutation statistics over any set of permutations whose quasisymmetric generating function is a symmetric function. Our formulas involve certain kinds of plethystic…

We prove that, for the quon algebra, which interpolates between the Bose and Fermi statistics and depends on a free parameter q,it is possible to build an su(2) irreducible representation. One of the consequences of this fact is that the…

We show that bosonization in two dimensions can be derived as a special case of the duality transformations that have recently been used to good effect in string theory. This allows the construction of the bosonic counterpart of any…

A brief presentation of basic definitions and notation used in permutation patterns research.

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes…

To speak about identical particles - bosons or fermions - in quantum field theories with kappa-deformed Poincare symmetry, one must have a kappa-covariant notion of particle exchange. This means constructing intertwiners of the relevant…

Multivariate meta-analysis is gaining prominence in evidence synthesis research because it enables simultaneous synthesis of multiple correlated outcome data, and random-effects models have generally been used for addressing between-studies…

In this article I expound an understanding of the quantum mechanics of so-called "indistinguishable" systems in which permutation invariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This…

Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal…

We prove a general version of the classical Perron-Frobenius convergence property for reducible matrices. We then apply this result to reducible substitutions and use it to produce limit frequencies for factors and hence invariant measures…

We present an extension of ``smooth bosonization'' to the non-Abelian case. We construct an enlarged theory containing both bosonic and fermionic fields which exhibits a local chiral gauge symmetry. A gauge fixing function depending on one…

Dokos et. al. studied the distribution of two statistics over permutations $\mathfrak{S}_n$ of $\{1,2,\dots, n\}$ that avoid one or more length three patterns. A permutation $\sigma\in\mathfrak{S}_n$ contains a pattern…

We introduce the notion of crossings and nestings of a permutation. We compute the generating function of permutations with a fixed number of weak exceedances, crossings and nestings. We link alignments and permutation patterns to these…

We present some Markovian approaches to prove universality results for some functions on the symmetric group. Some of those statistics are already studied in [Kammoun, 2018, 2020] but not the general case. We prove, in particular, that the…

Pairing between fermions that attract each other, reveal itself to the macroscopic world in the form of superfluidity. Since the discovery of fermionic superfluidity, intense search has been going on to find various unconventional forms of…

Using evaluation at appropriately chosen points, we propose a Gr\"obner basis free approach for calculating the secondary invariants of a finite permutation group. This approach allows for exploiting the symmetries to confine the…

Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, various formulations (equations, commutation relations, propagators, Jacobi identities,…

The many-anyons wavefunction is constructed via the superposition of all the permutations on the direct product of single anyon states and its interchange properties are examined. The phase of permutation is not a representation but the…

After a brief mention of Bose and Fermi oscillators and of particles which obey other types of statistics, including intermediate statistics, parastatistics, paronic statistics, anyon statistics and infinite statistics, I discuss the…