7 An antimatroid is a family of sets such that it contains an empty set, and it is accessible and closed under union of sets. An antimatroid is an ‘antipodal’ concept of matroid. 9 We shall show that an antimatroid is derived from shelling of a poset if and only if it does not contain a minor isomorphic to S7 where S7 is the smallest semimodular lattice that is not 11 modular. It is also shown ...

We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among graphs. (This is consequence general theorem proved L. Ham and M. Jackson, counterpart this for all in class well-known compactness theorem.) Also, to exemplify our method applicable various fields mathematics, we prove neither simple groups, nor ordered sets join-irre...

The paper describes a few ways in which the concept of a Coxeter group (in its most ubiquitous manifestation, the symmetric group) emerges in the theory of ordinary matroids: • Gale’s maximality principle which leads to the Bruhat order on the symmetric group; • Jordan–Hölder permutation which measures distance between two maximal chains in a semimodular lattice and which happens to be closely ...

For any ordered set P, the join dense completions of P form a complete lattice K(P) with least element O(P), the lattice of order ideals of P, and greatest element M(P), the Dedekind-MacNeille completion of P. The latticeK(P) is isomorphic to an ideal of the lattice of all closure operators on the lattice O(P). Thus it inherits some local structural properties which hold in the lattice of closu...

Shafer’s mathematical theory of evidence is one of the most remarkable attempts to introduce a complete generalized probability theory. One of its features is the central role of the notion of different level of knowledge of a given phenomenon, embodied into the idea of compatible frames of discernment . In this work we are going to analyze the algebraic basement of the concept of family of fra...