cp's OEIS Frontend

The fact that H is of odd order means H is disjoint from -H. The finite integral relation algebra with n pairs of asymmetric diversity atoms a_i, where the forbidden cycles are of the form (a_i, a_i, a_i^(converse)), is representable over Z/pZ, where p = a(n). These are "directed anti-Ramsey algebras", since "monochromatic intransitive triangles" are forbidden.

a(n) <= n^4 + 5 (cf. Alm, 2017).

The subgroup H, along with its n-1 cosets, induces a cyclic coloring on K_q. Labeling the vertices 0 through q-1, color the edge uv by the color corresponding to the coset containing u-v (mod q). Thus if q >= a(n), the coloring induced by H and its cosets must contain a monochromatic triangle. In fact, it contains many monochromatic triangles in each color class.

The data gathered thus far suggest that the bound n^4 + 5 can be replaced by cn^3 for some c > 1, but there is no proof.

a(n) > A263308(n). The reason A263308(8) is zero can be taken to be that a(8) is exceptionally small; similarly, a(13) is small, so A263308(13)=0.

a(n) <= n^4 + 5 (cf. Alm, 2017). There cannot be arbitrarily large multiplicative-coset Ramsey algebras in a fixed number of colors.

a(n) < A294676(n).