Pyrrole-based π-conjugated anion-responsive molecules bearing an anionic moiety form self-complementary dimers, which exhibit self-sorting behaviours depending on the substituted positions of anionic sites.

Abstract In this paper we give Pfaffian expressions and constant term identities for three conjectures (i.e. Conjecture 2, Conjecture 3 and Conjecture 7) by Mills, Robbins and Rumsey in the paper “Self-complementary totally symmetric plane partitions” J. Combin. Theory Ser. A 42, 277–292) concerning the refined enumeration problems of totally symmetric self-complementary plane partitions. We al...

Orthogonal matrices over arbitrary elds are de ned together with their non-square analogs, which are termed row-orthogonal matrices. Antiorthogonal and self-orthogonal square matrices are introduced together with their non-square analogs. The relationships of these matrices to such codes as self-dual codes and linear codes with complementary duals are given. These relationships are used to obta...

The complementary prism of a graph Γ is the ΓΓ̄, which formed from union and its complement Γ̄ by adding an edge between each pair identical vertices in Γ̄. Vertex-transitive self-complementary graphs provide vertex-transitive prisms. It was recently proved author that ΓΓ̄ core, i.e. all endomorphisms are automorphisms, whenever vertex-transitive, self-complementary, either core or complete graph. ...