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"Transformations"
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Congruence Lattices of Ideals in Categories and (Partial) Semigroups
This monograph presents a unified framework for determining the congruences on a number of monoids and categories of transformations,
diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain
normal subgroup lattices on top of each other to successively build congruence lattices of a chain of ideals. This is applied to several
specific categories of: transformations; order/orientation preserving/reversing transformations; partitions; planar/annular partitions;
Brauer, Temperley–Lieb and Jones partitions; linear and projective linear transformations; and partial braids. Special considerations
are needed for certain small ideals, and technically more intricate theoretical underpinnings for the linear and partial braid
categories.
eBook
Symmetric division degree index and inverse sum index of transformation graph
Topological Indices are the graph invariants, a real number obtained from a network (graph), used to characterize the structural properties of a network. In this paper, the general expression for Symmetric Division Degree index & Inverse Sum Index of the transformation networks of a network are obtained. Moreover, we find the expression for Symmetric Division Degree index & Inverse Sum Index of complement of transformation networks.
Journal Article
Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits
We study a class of measure-theoretic objects that we call
eBook