Related papers: Associative spectra of binary operations
The distance of an operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Associative spectra were introduced in a publication by B. Cs\'ak\'any and T. Waldhauser in…
We initiate the study of a quantitative measure for the failure of a binary operation to be commutative and associative. We call this measure the associative-commutative spectrum as it extends the so-called associative spectrum (also known…
The associative spectrum of a groupoid (i.e., a set with a binary operation) measures its nonassociativity while the associative-commutative spectrum measures both nonassociativity and noncommutativity of the groupoid. The two spectra are…
Characterizations of "almost associative" binary operations generating a minimal clone are given for two interpretations of the term "almost associative". One of them uses the associative spectrum, the other one uses the index of…
A necessary and sufficient condition is presented for a graph algebra to satisfy a bracketing identity. The associative spectrum of an arbitrary graph algebra is shown to be either constant or exponentially growing.
The adjacency operator of a graph has a spectrum and a class of scalar-valued spectral measures which have been systematically analyzed; it also has a spectral multiplicity function which has been less studied. The first purpose of this…
We explore the notion of degree of asymmetry for integer sequences and related combinatorial objects. The degree of asymmetry is a new combinatorial statistic that measures how far an object is from being symmetric. We define this notion…
Many functions have been recently defined to assess the similarity among networks as tools for quantitative comparison. They stem from very different frameworks - and they are tuned for dealing with different situations. Here we show an…
Binary hashing is a well-known approach for fast approximate nearest-neighbor search in information retrieval. Much work has focused on affinity-based objective functions involving the hash functions or binary codes. These objective…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string…
We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which…
A binary word is symmetric if it is a palindrome or an antipalindrome. We define a new measure of asymmetry of a binary word equal to the minimal number of letters of the word whose deleting from the word yields a symmetric word and obtain…
Associative spectra of graph algebras are examined with the help of homomorphisms of DFS trees. Undirected graphs are classified according to the associative spectra of their graph algebras; there are only three distinct possibilities:…
A certain analysis of all possible associative binary operations on N is presented. This is equivalent with an analysis of all possible monoid structures on N. Several results and a conjecture in this regard are given.
A pairing function for the non-negative integers is said to be binary perfect if the binary representation of the output is of length 2k or less whenever each input has length k or less. Pairing functions with square shells, such as the…
In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that,…
The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…
We determine the average number of distinct subsequences in a random binary string, and derive an estimate for the average number of distinct subsequences of a particular length.