The k-Young lattice Y k is a partial order on partitions with no part larger than k. This weak subposet of the Young lattice originated [9] from the study of the k-Schur functions s (k) λ , symmetric functions that form a natural basis of the space spanned by homogeneous functions indexed by k-bounded partitions. The chains in the k-Young lattice are induced by a Pieri-type rule experimentally ...

We give a necessary and su¢ cient condition for a bounded involution lattice to be isomorphic to the direct square of its invariant part. This result is applied to show relations between related lattices of an algebra: For instance, generalizing some earlier results of G. Czédli and L. Szabó it is proved that any algebra admits a connected compatible partial order whenever its quasiorder lattic...

An rj-normal lattice is a distributive lattice with 0 such that each prime ideal contains at most n minimal prime ideals. A relatively ra-normal lattice is a distributive lattice such that each bounded closed interval is an /¡.-normal lattice. The main results of this paper are: (1) a distributive lattice L with 0 is 71,-normal if and only if for any %n, x,,*•', X e L such that x Ax. = 0 for an...

We prove an exponential upper bound for the number f(m,n) of all maximal triangulations of the m × n grid: f(m,n) < 2. In particular, this improves a result of S. Yu. Orevkov [1]. We consider lattice polygons P (with vertices in Z), for example the convex hull of the grid Pm,n := {0, 1, . . . , m} × {0, 1, . . . , n}. We want to estimate the number of maximal lattice triangulations of P , i.e.,...

We prove that an infinite (bounded) involution lattice and even pseudo-Kleene algebra can have any number of congruences between 2 its elements or equalling subsets, regardless whether it has as many ideals subsets. Furthermore, when they at most elements, these lattices algebras be chosen such all their preserve involutions, so reducts. Under the Generalized Continuum Hypothesis, this means id...

An orthogonality space is a set equipped with symmetric, irreflexive relation called orthogonality. Every has an associated complete ortholattice, the logic of space. To every poset, we associate consisting proper quotients (that means, nonsingleton closed intervals), certain relation. We prove that finite bounded poset lattice if and only its orthomodular lattice. chain Boolean algebra.

Recently, the topic related to construction of triangular norms and conorms on bounded lattices using ordinal sums has been extensively studied. In this paper, we introduce a new sum an appropriate lattice. Also, give some illustrative examples for clarity. Then, show that method can be generalized by induction modified lattice, respectively. And provide examples.

We show that a commutative bounded integral orthomodular lattice is residuated iff it is a Boolean algebra. This result is a consequence of [7, Theorem 7.31]; however, our proof is independent and uses other instruments.

Double basic algebras are a counterpart of bounded lattices with orderantiautomorphisms on principal filters. In the paper, an independent axiomatization of double basic algebras is given and lattice pseudo-effect algebras are characterized in the setting of double basic algebras.

We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.