On the refined 3-enumeration of alternating sign matrices

F. Colomo; A. G. Pronko

Home/Archive/arXiv

arXiv · math-ph/0404045

On the refined 3-enumeration of alternating sign matrices

F. Colomo·A. G. Pronko

View original source ↗Read source document ↗Export metadata ↓

Abstract

An explicit expression for the numbers $A(n,r;3)$ describing the refined 3-enumeration of alternating sign matrices is given. The derivation is based on the recent results of Stroganov for the corresponding generating function. As a result, $A(n,r;3)$'s are represented as 1-fold sums which can also be written in terms of terminating ${}_4F_3$ series of argument 1/4.

Explore related subjects

math-ph hep-th math.CO math.MP

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

F. Colomo, A. G. Pronko. 2004-11-25. On the refined 3-enumeration of alternating sign matrices. https://arxiv.org/abs/math-ph/0404045

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Existence of a weak solution to the Navier-Stokes equations enjoying the energy equality

To date, a Leray's weak solution to the Navier-Stokes equations enjoys an energy inequality. We prove the existence of a weak solution that enjoys the energy equality. The existence of the weak solution is achieved as limit of solutions to the mollified Navier-Stokes system (Leray's approach). Since no uniqueness result is known for weak solutions we are not able to claim that any weak solution in the sense of Leray-Hopf enjoys the energy equality.

math-ph↗

arXiv2026

A Primer on Instanton Physics - A Short Course

These six lectures, delivered at the University of New Brunswick 6-21 October 2026, are an introduction to instantons in quantum mechanics and quantum field theory for senior undergraduate and beginning graduate students. The first four lectures deal solely with particle mechanics, building the necessary background for the last two that cover applications in semi-classical field theory.

math-ph↗

arXiv2026

Stochastic dynamics generation of directed percolation using a two-channel convolutional neural network

Neural networks provide a promising approach to learning and generating the stochastic dynamics of nonequilibrium systems. In this study, we propose a stochastic dynamics generative method based on a two-channel convolutional neural network, using the (1+1)-dimensional directed bond percolation model to investigate its ability to learn local stochastic transition rules and reproduce stochastic dynamics across different system sizes. The proposed method takes the current particle configuration and the control parameter as inputs, learns the conditional activation probabilities at the next time step through local convolutions, and generates stochastic temporal evolution through iterative Bernoulli sampling. The results show that the network-generated dynamics agree well with Monte Carlo simulations across different control parameters. Furthermore, applying the trained network to a substantially larger system with $L=10000$ yields an estimated critical probability of $p_c=0.643$ and an effective density decay exponent of $δ\approx0.1592$, close to the established theoretical values. These findings demonstrate that the proposed method can reproduce the stochastic dynamics of directed percolation and capture its macroscopic dynamical and statistical properties across different spatial sizes.

math-ph↗