A balanced part ternary design (BPTD) is a balanced ternary design (BTD) with a specified number of blocks, say b2, each having repeated elements. We prove some necessary conditions on b2 and show the existence of some particular BPTDs. We also give constructions of infinite families of BPTDs with b1 = 0, including families of ternary t-designs with t ≥ 3.

Let S be a complete star-omega semiring and Σ be an alphabet. For a weighted ω-pushdown automaton P with stateset {1, . . . ,n}, n ≥ 1, we show that there exists a mixed algebraic system over a complete semiring-semimodule pair ((S≪ Σ ≫),(S≪ Σ ≫)) such that the behavior ‖P‖ of P is a component of a solution of this system. In case the basic semiring is B or N we show that there exists a mixed c...

In the basic general frame of the Langlands global program, a local p -adic elliptic semimodule corresponding to a local (left) cuspidal form is constructed from it global equivalent covered by p roots. In the same context, global and local bilinear deformations of Galois representations inducing the invariance of their respective residue fields are introduced as well as global and local biline...

generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and   -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. some new results are obtained.

The blocks of a balanced ternary design, BTD(V,B; ρ1, ρ2, R;K,Λ), can be partitioned into two sets: the b1 blocks that each contain no repeated elements, and the b2 = B − b1 blocks containing repeated elements. In this note, we address, and answer in some particular cases, the following question. For which partitions of the integer B as b1 + b2 does there exist a BTD(V,B; ρ1, ρ2, R;K,Λ)?

Let (ωn)0<n be the sequence known as Integer Sequence A047749 In this paper, we show that the integer ωn enumerates various kinds of symmetric structures of order two. We first consider ternary trees having a reflexive symmetry and we relate all symmetric combinatorial objects by means of bijection. We then generalize the symmetric structures and correspondences to an infinite family of symmetr...