Related papers: Combinatorial study of colored Hurwitz polyz\^etas
This chapter combines an introduction and research survey about Schubert varieties. The theme is to combinatorially classify their singularities using a family of polynomial ideals generated by determinants.
We introduce two new binary operations with combinatorial species; the arithmetic product and the modified arithmetic product. The arithmetic product gives combinatorial meaning to the product of Dirichlet series and to the Lambert series…
In this paper, we give a general framework for the Boltzmann generation of colored objects belonging to combinatorial constructible classes. We propose an intuitive notion called profiled objects which allows the sampling of size-colored…
Schubert polynomials were introduced in the context of the geometry of flag varieties. This paper investigates some of the connections not yet understood between several combinatorial structures for the construction of Schubert polynomials;…
In this work, an extension of the generalized mixed Schwarz inequality is proved. A companion of the generalized mixed Schwarz inequality is established by merging both Cartesian and Polar decompositions of operators. Based on that some…
A barred preferential arrangement is a preferential arrangement onto which a number of identical bars are inserted in between the blocks of the preferential arrangement. In this study we examine combinatorial properties of barred…
Schubert polynomials are a basis for the polynomial ring that represent Schubert classes for the flag manifold. In this paper, we introduce and develop several new combinatorial models for Schubert polynomials that relate them to other…
In this paper we study the combinatorial consequences of the relationship between rational Cherednik algebras of type $G(l,1,n)$, cyclic quiver varieties and Hilbert schemes. We classify and explicitly construct $\mathbb{C}^*$-fixed points…
We show that the formalism of hybrid polynomials, interpolating between Hermite and Laguerre polynomials, is very useful in the study of Motzkin numbers and central trinomial coefficients. These sequences are identified as special values of…
We study a generalization of the Harish-Chandra - Itzykson - Zuber integral to tensors and its expansion over trace-invariants of the two external tensors. This gives rise to natural generalizations of monotone double Hurwitz numbers, which…
We give characterizations of the Borel sets potentially in some Wadge class, among the Borel sets with countable vertical sections of a product of two Polish spaces. To do this, we use some partial uniformization results.
We extend the old formalism of cut-and-join operators in the theory of Hurwitz $\tau$-functions to description of a wide family of KP-integrable {\it skew} Hurwitz $\tau$-functions, which include, in particular, the newly discovered…
In this paper, we study a certain type of Hurwitz numbers which count branched covers over the Riemann sphere admitting several branch points with fixed ramification types, one branch point with a fixed number of preimages, and one branch…
We study diverse parametrized versions of the operad of associative algebra, where the parameter are taken in an associative semigroup $\Omega$ (generalization of matching or family associative algebras) or in its cartesian square…
We express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix…
We present a proof of the compositional shuffle conjecture, which generalizes the famous shuffle conjecture for the character of the diagonal coinvariant algebra. We first formulate the combinatorial side of the conjecture in terms of…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
We define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions,…
The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to…
In this article we are introducing combinatorial spectra of graphs, this is a generalization of $H$-Hamiltonian spectra. The main motivation was to made from $H$-Hamiltonian spectra an operation and develop some algebra in this field. An…