Covariant presheaves and subalgebras.
The concept of covering energy of a poset is known and its McClelland type bounds are available in the literature. In this paper, we establish formulas for the covering energy of a crown with elements and a fence with elements. A lower bound for the largest eigenvalue of a poset is established. Using this lower bound, we improve the McClelland type bounds for the covering energy for some special classes of posets.
It is well known that the linear extension majority (LEM) relation of a poset of size can contain cycles. In this paper we are interested in obtaining minimum cutting levels such that the crisp relation obtained from the mutual rank probability relation by setting to its elements smaller than or equal to , and to its other elements, is free from cycles of length . In a first part, theoretical upper bounds for are derived using known transitivity properties of the mutual rank probability...
We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among finite graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the counterpart of this fact for all bipartite graphs in the class of all graphs is a well-known consequence of the compactness theorem.) Also, to exemplify that our method is applicable in various fields of mathematics, we prove that neither finite simple groups, nor the...
A representation of cyclically ordered sets by means of partial semigroups with an additional unary operation is constructed.
Rings of formal power series with exponents in a cyclically ordered group were defined in [2]. Now, there exists a “valuation” on : for every in and in , we let be the first element of the support of which is greater than or equal to . Structures with such a valuation can be called cyclically valued rings. Others examples of cyclically valued rings are obtained by “twisting” the multiplication in . We prove that a cyclically valued ring is a subring of a power series ring with...