Related papers: Spelling Rules for the Monster/Semple Tower
The Monster tower, also known as the Semple tower, is a sequence of manifolds with distributions of interest to both differential and algebraic geometers. Each manifold is a projective bundle over the previous. Moreover, each level is a…
We show the details of certain computations that are described in [BMW19].
We show the details of certain computations that are used in the paper "Verification of the conjugacy classes and ordinary character table of the Monster".
We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
We consider here the problem of classifying orbits of an action of the dif- feomorphism group of 3-space on a tower of fibrations with P2-fibers that generalize the Monster Tower due to Montgomery and Zhitomirskii. As a corollary we give…
This paper considers a problem that relates to the theories of covering arrays, permutation patterns, Vapnik-Chervonenkis (VC) classes, and probability thresholds. Specifically, we want to find the number of subsets of [n]:={1,2,....,n} we…
In this note we summarize our results from earlier work with the Monster Tower (A Monster Tower Approach to Goursat Multi-Flags). In particular, we give an overview of the problem of classifying the orbits within a tower of fibrations with…
Black holes at the TeV scale are investigated in the extra large dimension scenario. We interpret the lightest black hole excitation as a singlet scalar field, and show how interaction terms can be appended to the standard model at the…
This paper introduces the Primender sequence, a novel integer sequence defined by a hybrid rule that combines classical primality with modular digit-based conditions. Specifically, a number n is included in the sequence if it is prime or…
This is an experiential study of investigating a consistent method for deriving the correlation between sentence vector and semantic meaning of a sentence. We first used three state-of-the-art word/sentence embedding methods including…
Sequences of numbers (either natural integers, or integers or rational) of level $k \in \mathbb{N}$ have been defined in \cite{Fra05,Fra-Sen06} as the sequences which can be computed by deterministic pushdown automata of level $k$. This…
As a contribution to an eventual solution of the problem of determination of the maximal subgroups of the Monster we show that there is a unique conjugacy class of subgroups isomorphic to $PSU_3(8)$. The argument depends on some…
We employ the recently developed hybrid and mmgroup computational models for groups to calculate the character table of $N(\rm{2B}^5) \cong 2^{5+10+20}.( \rm{S}_3 \times \rm{L}_5 {2} )$, a maximal subgroup of the Monster sporadic simple…
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We…
A tower is a sequence of words alternating between two languages in such a way that every word is a subsequence of the following word. The height of the tower is the number of words in the sequence. If there is no infinite tower (a tower of…
Most adversarial attack methods that are designed to deceive a text classifier change the text classifier's prediction by modifying a few words or characters. Few try to attack classifiers by rewriting a whole sentence, due to the…
Mental health professionals and clinicians have observed the upsurge of mental disorders due to Interpersonal Risk Factors (IRFs). To simulate the human-in-the-loop triaging scenario for early detection of mental health disorders, we…
As part of the programme to re-compute the character tables of all the groups in the Atlas we re-compute the character table of $\mathbb M$, the Monster simple group. We operate under the uniqueness hypotheses of $\mathbb M$ and the…
A tower between two regular languages is a sequence of strings such that all strings on odd positions belong to one of the languages, all strings on even positions belong to the other language, and each string can be embedded into the next…