منابع مشابه
Lattices on simplicial partitions
In this paper, (d + 1)-pencil lattices on simplicial partitions in Rd are studied. The barycentric approach naturally extends the lattice from a simplex to a simplicial partition, providing a continuous piecewise polynomial interpolant over the extended lattice. The number of degrees of freedom is equal to the number of vertices of the simplicial partition. The constructive proof of this fact l...
متن کاملPartitions and Their Lattices
Ferrers graphs and tables of partitions are treated as vectors. Matrix operations are used for simple proofs of identities concerning partitions. Interpreting partitions as vectors gives a possibility to generalize partitions on negative numbers. Partitions are then tabulated into lattices and some properties of these lattices are studied. There appears a new identity counting isoscele Ferrers ...
متن کاملGeometric Lattices of Structured Partitions
*Research and preparation of this report were substantially assisted by National Science Foundation grants DMS-8407102 and DMS-8606102. For certain matroids on the edges of a graph, digraph, or bidirected graph with group gains (edge labels from a group), the ats form intriguing new geometric lattices whose Whitney numbers have geometrical signiicance. In this chapter, the rst of a series, we l...
متن کاملZeons, Lattices of Partitions, and Free Probability
Central to the theory of free probability is the notion of summing multiplicative functionals on the lattice of non-crossing partitions. In this paper, a graph-theoretic perspective of partitions is investigated in which independent sets in graphs correspond to non-crossing partitions. By associating particular graphs with elements of “zeon” algebras (commutative subalgebras of fermion algebras...
متن کاملFaa' di Bruno's formula, lattices, and partitions
The coefficients of g(s) in expanding the rth derivative of the composite function g ◦ f by Faà di Bruno’s formula, is determined by a Diophantine linear system, which is proved to be equivalent to the problem of enumerating partitions of a finite set of integers attached to r and s canonically. © 2005 Elsevier B.V. All rights reserved. MSC: primary 11D04; secondary 05A17; 11D45; 11Y50; 15A36; ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Sciences
سال: 2007
ISSN: 1812-5654
DOI: 10.3923/jas.2007.2366.2370