相关论文: Isonemal Prefabrics with Perpendicular Axes of Sym…
This paper refines Richard Roth's taxonomy of isonemal weaving designs through the final types 33--39 in order to complete the solution of three problems for those designs: which designs exist in various sizes, which prefabrics can be…
Isonemal weaving designs, introduced into mathematical literature by Gr\"unbaum and Shephard, were classified into thirty-nine infinite sets and a small number of exceptions by Richard Roth. This paper refines Roth's taxonomy for the first…
Perfect colouring of isonemal fabrics by thick striping of warp and weft and the closely related topic of isonemal prefabrics that fall apart are reconsidered and their relation further explored. The catalogue of isonemal prefabrics of…
Perfect colouring of isonemal fabrics by thin striping of warp and weft and the closely related topic of isonemal prefabrics that fall apart are reconsidered and their relation further explored. The catalogue of isonemal prefabrics that…
Perfect colouring of isonemal fabrics by thin and thick striping of warp and weft with more than two colours is examined where the cells with warps and wefts of the same colour do not appear along diagonal lines (not twilly redundancy). In…
The parameters 2-(36,15,6) are the smallest parameters of symmetric designs for which a complete classification up to isomorphism is yet unknown. Bouyukliev, Fack and Winne classified all 2-$(36,15,6)$ designs that admit an automorphism of…
We discuss the isomorphism problem of projective schemes; given two projective schemes, can we algorithmically decide whether they are isomorphic? We give affirmative answers in the case of one-dimensional projective schemes, the case of…
A triangulation of a punctured or pinched surface is irreducible if no edge can be shrunk without producing multiple edges or changing the topological type of the surface. The finiteness of the set of (non-isomorphic) irreducible…
We compute all isomorphism classes of simplicial arrangements in the real projective plane with up to 27 lines. It turns out that Gr\"unbaums catalogue is complete up to 27 lines except for four new arrangements with 22, 23, 24, 25 lines,…
The complete sets of irreducible triangulations are known for the orientable surfaces with genus of 0, 1, or 2 and for the nonorientable surfaces with genus of 1, 2, 3, or 4. By examining these sets we determine some of the properties of…
A triangulation of a surface with fixed topological type is called irreducible if no edge can be contracted to a vertex while remaining in the category of simplicial complexes and preserving the topology of the surface. A complete list of…
This paper considers affine analogues of the isoperimetric inequality in the sense of piecewise linear topology. Given a closed polygon P embedded in R^d having n edges, we give upper and lower bounds for the minimal number of triangles…
The largest prime p that can be the order of an automorphism of a 2-(35,17,8) design is p=17, and all 2-(35,17,8) designs with an automorphism of order 17 were classified by Tonchev. The symmetric 2-(35,17,8) designs with automorphisms of…
Quandles with involutions that satisfy certain conditions, called good involutions, can be used to color non-orientable surface-knots. We use subgroups of signed permutation matrices to construct non-trivial good involutions on extensions…
We show that permutations of size $n$ avoiding both of the dashed patterns 32-41 and 41-32 are equinumerous with indecomposable set partitions of size $n+1$, and deduce a related result.
We initiate the study of limit shapes for random permutations avoiding a given pattern. Specifically, for patterns of length 3, we obtain delicate results on the asymptotics of distributions of positions of numbers in the permutations. We…
We show that convex pentagons that can generate edge-to-edge monohedral tilings of the plane can be classified into exactly eight types. Using these results, it is also proved that no single convex polygon can be an aperiodic prototile…
There are four non-isomorphic configurations of triples that can form a triangle in a $3$-uniform hypergraph. Forbidding different combinations of these four configurations, fifteen extremal problems can be defined, several of which already…
We conclude the classification of isoparametric (or equivalently, polar) foliations of complex and quaternionic projective spaces. This is done by investigating the projections of certain inhomogeneous isoparametric foliations of the…
In contrast to many known results concerning periodic tilings of the Euclidean plane with pentagons, here tilings with rotational symmetry are investigated. A certain class of convex pentagons is introduced. It can be shown that for any…