A note on the birational geometry of tropical line bundles

Given a closed subvariety Y of a n-dimensional torus, we study how the tropical line bundles of Trop(Y) can be induced by line bundles living on a tropical compactification of Y in a toric variety, following the construction of Jenia Tevelev. We then consider the general structure with respect to the Zariski--Riemann space.Comment: Version

Ruled Fano fivefolds of index two

We classify Fano fivefolds of index two which are projectivization of rank two vector bundles over four dimensional manifolds.Comment: 30 page

The forgotten monoid

We study properties of the forgotten monoid which appeared in work of Lascoux and Schutzenberger and recently resurfaced in the construction of dual equivalence graphs by Assaf. In particular, we provide an explicit characterization of the forgotten classes in terms of inversion numbers and show that there are n^2-3n+4 forgotten classes in the symmetric group S_n. Each forgotten class contains a canonical element that can be characterized by pattern avoidance. We also show that the sum of Gessel's quasi-symmetric functions over a forgotten class is a 0-1 sum of ribbon-Schur functions.Comment: 13 pages; in version 3 the proof of Proposition 3 is correcte

Consumers' Willingness to Pay a Price for Organic Beef Meat

The goal of this paper is to estimate the maximum price consumers are willing to pay (MPWTP) for organic beef meat. To this purpose, a theoretical and econometric approach is presented, based on the RUM model and on a Contingent Valuation technique. The results show that consumers' MPWTP is quite high, thus suggesting that organic beef meat might gain an appreciable market share. This is also an encouraging signal for prospective producers of organic meat, who might compensate the likely increase in production costs with a substantial premium for the new good.Organic meat, Willingness to pay, Double bounded probit, Consumer/Household Economics,

Hopf Algebras of m-permutations, (m+1)-ary trees, and m-parking functions

The m-Tamari lattice of F. Bergeron is an analogue of the clasical Tamari order defined on objects counted by Fuss-Catalan numbers, such as m-Dyck paths or (m+1)-ary trees. On another hand, the Tamari order is related to the product in the Loday-Ronco Hopf algebra of planar binary trees. We introduce new combinatorial Hopf algebras based on (m+1)-ary trees, whose structure is described by the m-Tamari lattices. In the same way as planar binary trees can be interpreted as sylvester classes of permutations, we obtain (m+1)-ary trees as sylvester classes of what we call m-permutations. These objects are no longer in bijection with decreasing (m+1)-ary trees, and a finer congruence, called metasylvester, allows us to build Hopf algebras based on these decreasing trees. At the opposite, a coarser congruence, called hyposylvester, leads to Hopf algebras of graded dimensions (m+1)^{n-1}, generalizing noncommutative symmetric functions and quasi-symmetric functions in a natural way. Finally, the algebras of packed words and parking functions also admit such m-analogues, and we present their subalgebras and quotients induced by the various congruences.Comment: 51 page

Ideal Family Size and Fertility in Egypt: An Overview of Recent Trends

Egypt is already the most populous Arab country in the world with 93 million citizens in 2016 which may grow to about 120 million by 2030 if the same level of fertility continues. This paper aims to offer an overview of the evolution over time of the ideal number of children in Egypt, assessing previous researches and giving a particular emphasis on most recent data on such topic. In a context of raising fertility, whose causes are still unknown, we test the persistence of a high ideal number of children among younger cohorts

Superization and (q,t)-specialization in combinatorial Hopf algebras

We extend a classical construction on symmetric functions, the superization process, to several combinatorial Hopf algebras, and obtain analogs of the hook-content formula for the (q,t)-specializations of various bases. Exploiting the dendriform structures yields in particular (q,t)-analogs of the Bjorner-Wachs q-hook-length formulas for binary trees, and similar formulas for plane trees.Comment: 30 page