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Abstract: The set of all transformation monoids on a fixed set of infinite cardinality lambda, equipped with the order of inclusion, forms an algebraic lattice Mon(lambda) with 2^lambda compact elemen...
We study a model of self propelled particles exhibiting run-and-tumble dynamics on lattice. This non-Brownian di usion is characterised by a random walk with a nite persistence length between changes...
The lattice polynomials $L_{i,j}(x)$ are introduced by Hough and Shapiro as a weighted count of certain lattice paths from the origin to the point $(i,j)$. In particular, $L_{2n, n}(x)$ reduces to th...
We show that if G is a finite group then no chain of modular elements in its subgroup lattice L(G) is longer than a chief series. Also, we show that if G is a nonsolvable finite group then every maxi...
Elliptic N-soliton-type solutions, i.e. solutions emerging from the application of N consecutive B\"acklund transformations to an elliptic seed solution, are constructed for all equations in the ABS l...
Lattices in three dimensions are oft studied from the ``reciprocal space'' perspective of diffraction. Today, the full lattice of a crystal can often be inferred from direct-space information about t...

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