In this paper we study relations between intersection numbers on moduli spaces of curves and Hurwitz numbers. First, we prove two formulas expressing Hurwitz numbers of (generalized) polynomials via intersections on moduli spaces of curves. Then we show, how intersection numbers can be expressed via Hurwitz numbers. And then we obtain an algorithm expressing intersection numbers 〈τn,m ∏r−1 i=1 ...

We clarify the explicit structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory and systolic geometry. We present some properties of the associated congruence subgroups. Namely, we show that a Hurwitz group defined by a congruence subgroup associated with an odd ideal, is necessarily defined by a principal congruence subgroup. All such Hurwitz gro...

In this paper, a novel fractional-order 2I2SR rumor spreading model is investigated. Firstly, the boundedness and uniqueness of solutions are proved. Then next-generation matrix method used to calculate threshold. Furthermore, stability rumor-free/spreading equilibrium discussed based on Routh–Hurwitz criterion, Lyapunov function method, invariance principle. Next, necessary conditions for frac...

Applied science and mechanics need mathematical methods for 2D processes modeling using the set of data points. A novel method of Hurwitz-Radon Matrices (MHR) is used in 2D curve modeling. Proposed method is based on the family of Hurwitz-Radon matrices which possess columns composed of orthogonal vectors. Two-dimensional process is modeled via different functions: sine, cosine, tangent, logari...

Applied science and mechanics need mathematical methods for 2D processes modeling using the set of data points. A novel method of Hurwitz-Radon Matrices (MHR) is used in 2D curve modeling. Proposed method is based on the family of Hurwitz-Radon matrices which possess columns composed of orthogonal vectors. Two-dimensional process is modeled via different functions: sine, cosine, tangent, logari...

Applied science and mechanics need mathematical methods for 2D processes modeling using the set of data points. A novel method of Hurwitz-Radon Matrices (MHR) is used in 2D curve modeling. Proposed method is based on the family of Hurwitz-Radon matrices which possess columns composed of orthogonal vectors. Two-dimensional process is modeled via different functions: sine, cosine, tangent, logari...

In this paper, we prove that the Hurwitz equivalence problem for 1-factorizations in F2⊕F2 is undecidable, and as a consequence, the Hurwitz equivalence problem for ∆-factorizations in the braid groups Bn, n ≥ 5 is also undecidable.

We identify the normal subgroups of the orientation preserving subgroup [3, 5, 3] of the Coxeter group [3, 5, 3], with the factor group isomorphic to PSL2(Fq) with particular congruence subgroups of an arithmetic subgroup of PSL2(C) derived from a quaternion algebra over a quartic field. 1 Motivation – Hurwitz groups and HurwitzMacbeath surfaces It is a well known fact that up to isomorphy, the...

We prove that the free energy of the Harish-Chandra-Itzykson-Zuber matrix model admits an N → ∞ asymptotic expansion in powers of N −2 whose coefficients are generating functions for a desymmetrized version of the double Hurwitz numbers, which we call monotone double Hurwitz numbers. Thus, the HCIZ free energy expands as a generating function enumerating certain branched covers of the Riemann s...