Hereditarily Odd–even and Combinatorial Isols
نویسندگان
چکیده
In this paper we study some of the arithmetic structure that is found in a special kind of semi-ring in the isols. These are the semi-rings [D(Y ),+, ·] that were introduced by J.C.E. Dekker, and that were later shown by E. Ellentuck to model the true universal recursive statements of arithmetic when Y is a regressive isol and is hyper-torre (= hereditarily odd-even = HOE). When Y is regressive and HOE, we further reflect on the structure of D(Y ). In addition, a new variety of regressive isol is introduced, called combinatorial. When Y is such an isol, then it is also HOE, and more, and the arithmetic of D(Y ) is shown to have a richer structure.
منابع مشابه
Geometric Characterization of Hereditarily Bijective Boolean Networks
The study of relationships between structure and dynamics of asynchronous Boolean networks has recently led to the introduction of hereditarily bijective maps and even or odd self-dual networks. We show here that these two notions can be simply characterized geometrically: through orthogonality between certain affine subspaces. We also use this characterization to provide a construction of the ...
متن کاملHereditarily Separable Groups and Monochromatic Uniformization
We give a combinatorial equivalent to the existence of a non-free hereditarily separable group of cardinality א1. This can be used, together with a known combinatorial equivalent of the existence of a non-free Whitehead group, to prove that it is consistent that every Whitehead group is free but not every hereditarily separable group is free. We also show that the fact that Z is a p.i.d. with i...
متن کاملSkolem Odd Difference Mean Graphs
In this paper we define a new labeling called skolem odd difference mean labeling and investigate skolem odd difference meanness of some standard graphs. Let G = (V,E) be a graph with p vertices and q edges. G is said be skolem odd difference mean if there exists a function f : V (G) → {0, 1, 2, 3, . . . , p + 3q − 3} satisfying f is 1−1 and the induced map f : E(G) → {1, 3, 5, . . . , 2q−1} de...
متن کاملCombinatorial Hopf Algebras and Generalized Dehn-sommerville Relations
A combinatorial Hopf algebra is a graded connected Hopf algebra over a field k equipped with a character (multiplicative linear functional) ζ : H → k. We show that the terminal object in the category of combinatorial Hopf algebras is the algebra QSym of quasi-symmetric functions; this explains the ubiquity of quasi-symmetric functions as generating functions in combinatorics. We illustrate this...
متن کاملAsymptotic Behavior of Odd-Even Partitions
Andrews studied a function which appears in Ramanujan’s identities. In Ramanujan’s “Lost” Notebook, there are several formulas involving this function, but they are not as simple as the identities with other similar shape of functions. Nonetheless, Andrews found out that this function possesses combinatorial information, odd-even partition. In this paper, we provide the asymptotic formula for t...
متن کامل