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On Galois covers of a union of Zappatic surfaces of type $R_k$
We investigate the topological structures of Galois covers of a union of two Zappatic surfaces of type $R_k$. We prove that the Galois covers of such surfaces are simply-connected surfaces of general type. We also compute their ... Read More >
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$3$D Farey graph, lambda lengths and $SL_2$-tilings
We explore a three-dimensional counterpart of the Farey tessellation and its relations to Penner's lambda lengths and $SL_2$-tilings. In particular, we prove a three-dimensional version of Ptolemy relation, and generalise result ... Read More >
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A study on free roots of Borcherds-Kac-Moody Lie Superalgebras
Let $\mathfrak g$ be a Borcherds-Kac-Moody Lie superalgebra (BKM superalgebra in short) with the associated graph $G$. Any such $\mathfrak g$ is constructed from a free Lie superalgebra by introducing three different sets of rel ... Read More >
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Classification of P-oligomorphic groups, conjectures of Cameron and Macpherson
Let G be a group of permutations of a denumerable set E. The profile of G is the function phi which counts, for each n, the number phi(n) of orbits of G acting on the n-subsets of E. Counting functions arising this way, and thei ... Read More >
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Subpolygons in Conway-Coxeter frieze patterns
Friezes with coefficients are maps assigning numbers to the edges and diagonals of a regular polygon such that all Ptolemy relations for crossing diagonals are satisfied. Among these, the classic Conway-Coxeter friezes are the o ... Read More >
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The Möbius Function of the Affine Linear Group $\text{AGL}(1,\Bbb F_q)$
Let $\text{AGL}(1,\Bbb F_q)$ denote the affine linear group of dimension one over the finite field $\Bbb F_q$. We determine the M\"obius function of the lattice of subgroups of $\text{AGL}(1,\Bbb F_q)$. Read More >
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A Multiparametric Quon Algebra
The quon algebra is an approach to particle statistics introduced by Greenberg in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. We generalize these models by ... Read More >
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A mathematical perspective on the phenomenology of non-perturbative Quantum Fiel ...
This monograph aims to build some new mathematical structures originated from Dyson--Schwinger equations for the description of non-perturbative aspects of gauge field theories whenever bare or running coupling constants are str ... Read More >
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On simultaneous conjugation of permutations
In this paper we give an affirmative answer to a conjecture proposed by Danny Neftin, that is, if the commutator of two permutations has at least n-4 fixed points where two permutations are in degree n symmetric group, then ther ... Read More >
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A note on regular subgroups of the automorphism group of the linear Hadamard cod ...
We consider the regular subgroups of the automorphism group of the linear Hadamard code. These subgroups correspond to the regular subgroups of $GA(r,2)$, w.t.r action on the vectors of $F_2^{r}$, where $n=2^r-1 $ is the length ... Read More >