# Combinatorics of 3D directed animals on a simple cubic lattice

@article{Nechaev2020CombinatoricsO3, title={Combinatorics of 3D directed animals on a simple cubic lattice}, author={Sergei Nechaev and M. V. Tamm}, journal={arXiv: Statistical Mechanics}, year={2020} }

We provide combinatorial arguments based on a two-dimensional extension of a locally-free semigroup allowing us to compute the growth rate, $\Lambda$, of the partition function $Z_N=N^{\theta}\Lambda^N$ of the $N$-particle directed animals ($N\gg 1$) on a simple cubic lattice in a three-dimensional space. Establishing the bijection between the particular configuration of the lattice animal and a class of equivalences of words in the 2D projective locally-free semigroup, we find we find $\ln…

## References

SHOWING 1-10 OF 13 REFERENCES

### Robust Point Set Registration Using Gaussian Mixture Models

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2011

This paper presents a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers, and shows that the popular iterative closest point (ICP) method and several existing point setRegistration methods in the field are closely related and can be reinterpreted meaningfully in this general framework.

### Airways obstruction, chronic expectoration, and rapid decline of FEV1 in smokers are associated with increased levels of sputum neutrophils.

- MedicineThorax
- 1996

BACKGROUND: Smoking may cause inflammation of the airways and impairment of lung function. To determine the relationship between the type and degree of airways inflammation and the decline in lung…

### Bellman Error Based Feature Generation using Random Projections on Sparse Spaces

- Computer ScienceNIPS
- 2013

A simple, fast and robust algorithm based on random projections, which generates Bellman Error Basis Functions for sparse feature spaces, and proves that projections logarithmic in the dimension of the original space guarantee a contraction in the error.

### Phaseless inverse scattering and the phase problem in optics

- Mathematics
- 1992

Two related problems are considered: (i) the inverse scattering problem for a potential V(x) supported on the half‐line {x≥0}, when the given data is ‖R−(k)‖, the amplitude of the reflection…

### GENERALIZABILITY AND AUTOMATICITY OF SECOND LANGUAGE LEARNING UNDER IMPLICIT, INCIDENTAL, ENHANCED, AND INSTRUCTED CONDITIONS

- Linguistics
- 1997

This experimental study examines the extent to which 60 adult Japanese ESL learners were able to acquire a rule regulating the argument structure frames of novel verbs of English after exposure to…

### Statistical Properties of Locally Free Groups¶with Applications to Braid Groups¶and Growth of Random Heaps

- Mathematics
- 2000

Abstract: The main statistical characteristics of locally free groups: the growth, the drift and the entropy are considered and relations between them are established. Our results assert that: (i)…

### Exact solution of a 1d asymmetric exclusion model using a matrix formulation

- Mathematics
- 1993

Several recent works have shown that the one-dimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, can be…

### Exact Solution of a Directed-Site Animals-Enumeration Problem in three Dimensions.

- Mathematics
- 1983

An exact equivalence is established between the directed-site animals-enumeration (DSAE) problem in $d$ dimensions and a crystal-growth model defined on the same lattice. In special cases, the latter…

### Changes in membrane hydrogen and sodium conductances during progesterone-induced maturation of Ambystoma oocytes.

- BiologyDevelopmental biology
- 1984