Lattice Theory of Generalized Partitions

Theory of Generalized Piezoporo Thermoelasticity

In this paper, the basic constitutive equations and equations of motion are derived to describe the behavior of thermoelastic porous piezoelectric medium by using Biot’s theory and the theory of generalized thermoelasticity with on relaxation time (Lord-Shulman). The electrical enthalpy density function is derived in the general coordinates. Also, clear definitions for the poroelastic modulus, ...

Partitions of Generalized Split Graphs

We discuss matrix partition problems for graphs that admit a partition into k independent sets and ` cliques. We show that when k + ` 6 2, any matrix M has finitely many (k, `) minimal obstructions and hence all of these problems are polynomial time solvable. We provide upper bounds for the size of any (k, `) minimal obstruction when k = ` = 1 (split graphs), when k = 2, ` = 0 (bipartite graphs...

Generalized Integer Partitions , Tilings of

Jagged partitions and lattice paths

A lattice-path description of K-restricted jagged partitions is presented. The corresponding lattice paths can have peaks only at even x coordinate and the maximal value of the height cannot be larger than K − 1. Its weight is twice that of the corresponding jagged partitions. The equivalence is demonstrated at the level of generating functions. A bijection is given between K-restricted jagged ...

The lattice of finite subspace partitions

Let V denote V (n, q), the vector space of dimension n over GF(q). A subspace partition of V is a collection Π of subspaces of V such that every nonzero vector in V is contained in exactly one subspace belonging to Π. The set P(V ) of all subspace partitions of V is a lattice with minimum and maximum elements 0 and 1 respectively. In this paper, we show that the number of elements in P(V ) is c...