We address the enumeration of p-valent planar maps equipped with a spanning forest, with a weight z per face and a weight u per component of the forest. Equivalently, we count regular maps equipped with a spanning tree, with a weight z per face and a weight μ := u+ 1 per internally active edge, in the sense of Tutte. This enumeration problem corresponds to the limit q → 0 of the q-state Potts m...

In Part I of [3], Adaricheva and Nation introduced a new property that holds (dually) for the natural equaclosure operator on congruence lattices of semilattices with operators, and hence holds in lattices of quasivarieties Lq(K). The new property implied some previously known conditions as well. Using the duality for congruences of semilattices with operators from [7], we will refine that to a...

We investigate the homotopy type of space tuples polynomials inducing base-point preserving algebraic maps from circle S 1 to a toric variety X Σ . In particular, we prove stability result for this by combining Vassiliev spectral sequence [23] and scanning map [22]

We solve three enumerative problems concerning the families of planar maps. More precisely, we establish algebraic equations for the generating function of loopless triangulations in which all vertices have degree at least d, for a certain value d chosen in {3, 4, 5}. The originality of the problem lies in the fact that degree restrictions are placed both on vertices and faces. Our proofs first...

A Riemann–Roch theorem is a theorem which asserts that some algebraically defined wrong–way map in K –theory agrees or is compatible with a topologically defined one [BFM]. Bismut and Lott [BiLo] proved a Riemann–Roch theorem for smooth fiber bundles in which the topologically defined wrong–way map is the homotopy transfer of Becker–Gottlieb and Dold. We generalize and refine their theorem. In ...

Abstract. The semi-topological K-theory K ∗ (X) of a quasi-projective complex algebraic variety X is based on the notion of algebraic vector bundles modulo algebraic equivalence. This theory is given as the homotopy groups of an infinite loop space K(X) which is equipped with maps K(X) → K(X), K(X) → Ktop(Xan) whose composition is the natural map from the algebraic K-theory of X to the topologi...

We introduce the notions of strongly zero-product (strongly Jordan zero-product) preserving maps on normed algebras. These notions are generalization of the concepts of zero-product and Jordan zero-product preserving maps. Also for a non-zero vector space V and for a non-zero linear functional f on V, we equip V with a multiplication, converting V into an associative algebra, denoted by Vf . We...

×ØÖÖغ In the present paper, we present a slightly strengthened version of a well-known theorem of Belyi on the existence of " Belyi maps ". Roughly speaking, this strengthened version asserts that there exist Belyi maps which are unramified at [cf. Theorem 2.5] — or even near [cf. Corollary 3.2] — a prescribed finite set of points. Write C for the complex number field; Q ⊆ C for the subfield o...

Relative exactness modulo a polynomial map and algebraic (C p , +)-actions Abstract Let F = (f 1 , .., f q) be a polynomial dominating map from C n to C q. In this paper we study the quotient T 1 (F) of polynomial 1-forms that are exact along the generic fibres of F , by 1-forms of type dR + a i df i , where R, a 1 , .., a q are polynomials. We prove that T 1 (F) is always a torsion C[t 1 , ......

We extend the target map, together with the weighted barriers and the notions of weighted analytic centers, from linear programming to general convex conic programming. This extension is obtained from a novel geometrical perspective of the weighted barriers, that views a weighted barrier as a weighted sum of barriers for a strictly decreasing sequence of faces. Using the Euclidean Jordan-algebr...