We consider maps on genus-$g$ surfaces with $n$ (labeled) faces of prescribed even degrees. It is known since work Norbury that, if one disallows vertices degree one, the enumeration such related to counting lattice point in moduli space curves labeled points and given by a symmetric polynomial $N_{g,n}(\ell_1,\ldots,\ell_n)$ face degrees $2\ell_1, \ldots, 2\ell_n$. generalize this restricting ...

We show that two essentially conditional linear information inequalities (including the Zhang–Yeung’97 conditional inequality) do not hold for asymptotically entropic points. This result raises the question of the “physical” meaning of these inequalities and the validity of their use in practice-oriented applications.

In this paper we address some of the most fundamental questions regarding the diierentiability structure of locally Lipschitz functions deened on Banach spaces. For example, we examine the relationship between inte-grability, D-representability and strict diierentiability. In addition to this, we show that on a large class of Banach spaces there is a signiicant family of locally Lipschitz funct...

An important desideratum in priority-based allocation is stability : no agent should claim an object because she has higher priority than the agent to whom it is assigned. However, stable matchings are in general Pareto inefficient, forcing upon designers a difficult trade-off. This paper alleviates this tension between efficiency and stability by defining an assignment to be essentially stable...

Abstract In the language $$\lbrace 0, 1, \circ , \preceq \rbrace $$ { 0 , 1 ? ? } where 0 and 1 are constant symbols, $$\circ is a binary function symbol $$\preceq relation symbol, we f...

Many Hilbert modules over the polynomial ring in m variables are essentially reductive, that is, have commutators which are compact. Arveson has raised the question of whether the closure of homogeneous ideals inherit this property and provided motivation to seek an affirmative answer. Positive results have been obtained by Arveson, Guo, Wang and the author. More recently, Guo and Wang extended...