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We show that the number Z of q-edge-colourings of a simple regular graph of degree q is deducible from functions describing dimers on the same graph, viz. the dimer generating function or equivalently the set of connected dimer correlation…
While the light-front quark model (LFQM) is employed to calculate hadronic transition matrix elements, the vertex functions must be pre-determined. In this work we derive the vertex functions for all d-wave states in this model. Especially,…
In this note we obtain numerous new bases for the algebra of symmetric functions whose generators are chromatic symmetric functions. More precisely, if $\{ G_ k \}_{k\geq 1}$ is a set of connected graphs such that $G_k$ has $k$ vertices for…
Polysymmetric functions, introduced by Asvin G and Andrew O'Desky as a generalization of symmetric functions, have natural connections to algebraic geometry and provide a foundation for further developments. In this paper, we study…
The investigation of colour symmetries for periodic and aperiodic systems consists of two steps. The first concerns the computation of the possible numbers of colours and is mainly combinatorial in nature. The second is algebraic and…
We rewrite the (extended) Ooguri-Vafa partition function for colored HOMFLY-PT polynomials for torus knots in terms of the free-fermion (semi-infinite wedge) formalism, making it very similar to the generating function for double Hurwitz…
In this contribution we generalize the classical Fourier Mellin transform [S. Dorrode and F. Ghorbel, Robust and efficient Fourier-Mellin transform approximations for gray-level image reconstruction and complete invariant description,…
Using vertex operator we study Macdonald symmetric functions of rectangular shapes and their connection with the q-Dyson Laurent polynomial. We find a vertex operator realization of Macdonald functions and thus give a generalized Frobenius…
Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+1 and 3+1D are explored. Many of our field theories are highly-interacting without free quadratic analogs.…
Representing fermionic wavefunctions efficiently is a central problem in quantum physics, chemistry and materials science. In this work, we introduce a universal and exact representation of continuous antisymmetric functions by lifting them…
Unitary matrix integrals over symmetric polynomials play an important role in a wide variety of applications, including random matrix theory, gauge theory, number theory, and enumerative combinatorics. We derive novel results on such…
We couple two copies of the supersymmetric mKdV hierarchy by means of the algebraic dressing technique. This allows to deduce the whole set of $(N,N)$ supersymmetry transformations of the relativistic sector of the extended mKdV hierarchy…
Starting from the Verma module of U_q sl(2) we consider the evaluation module for affine U_q sl(2) and discuss its crystal limit (q=0). There exists an associated integrable statistical mechanics model on a square lattice defined in terms…
A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean…
Properties of the four families of recently introduced special functions of two real variables, denoted here by $E^\pm$, and $\cos^\pm$, are studied. The superscripts $^+$ and $^-$ refer to the symmetric and antisymmetric functions…
It is known that a subset of fractional quantum Hall wave functions has been expressed as conformal field theory (CFT) correlators, notably the Laughlin wave function at filling factor $\nu=1/m$ ($m$ odd) and its quasiholes, and the…
We define a family of symmetric and a family of non-symmetric polynomials in terms of vanishing conditions. These families depend on two paramters, q and t. Their main feature is that they consist of non-homogeneous polynomials. The…
Let $\Lambda$ be the space of symmetric functions and $V_k$ be the subspace spanned by the modified Schur functions $\{S_\lambda[X/(1-t)]\}_{\lambda_1\leq k}$. We introduce a new family of symmetric polynomials,…
We extend Zirnbauer's color-flavor transformation in the fermionic sector to the case of the special unitary group. The transformation allows a certain integral over SU(N_c) color matrices to be transformed into an integral over flavor…
We discuss several PT-symmetric deformations of superderivatives. Based on these various possibilities, we propose new families of complex PT-symmetric deformations of the supersymmetric Korteweg-de Vries equation. Some of these new models…