The enumeration of self-orthogonal Latin squares (SOLS) of a given order seems to be an open problem in the literature on combinatorial designs. The existence of at least one SOLS is guaranteed for any order except 2, 3 and 6, but it is not known how many of these squares of a given order exist. In this talk we present enumeration tables of unequal SOLS, idempotent SOLS, isomorphism classes of ...

We show that there exists a real non-singular pseudoholomorphic sextic curve in the affine plane which is not isotopic to any real algebraic sextic curve. This result completes the isotopy classification of real algebraic affine M -curves of degree 6. Comparing this with the isotopy classification of real affine pseudoholomorphic sextic M -curves obtained earlier by the first author, we find th...

Let Hg be a genus g handlebody and MCG2n(Tg) be the group of the isotopy classes of orientation preserving homeomorphisms of Tg = ∂Hg, fixing a given set of 2n points. In this paper we find a finite set of generators for E 2n, the subgroup of MCG2n(Tg) consisting of the isotopy classes of homeomorphisms of Tg admitting an extension to the handlebody and keeping fixed the union of n disjoint pro...

Latin tableaux are a generalization of squares, which first appeared in the early 2000's paper Chow, Fan, Goemans, and Vondrák. Here, we extend notion isotopy, permutation group action, from squares to tableaux. We define isotopy graphs for tableaux, encode structure orbits under investigate relationship between shape tableau its graph. Our main result shows that any positive integer d, there i...