We study a q-analog Qr(n, q) of the partition algebra Pr(n). The algebra Qr(n, q) arises as the centralizer algebra of the finite general linear group GLn(Fq) acting on a vector ...
For every k and r, we construct a finite family of axis-parallel rectangles in the plane such that no matter how we color them with k colors, there exists a point covered by prec...
A self-avoiding walk (SAW) on the square lattice is prudent if it never takes a step towards a vertex it has already visited. Prudent walks differ from most classes of SAW that ha...