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

Willingness-to-pay in terms of price: an application to organic beef during and after the “mad cow” crisis

This paper aims at assessing consumers’ attitudes and willingness to pay for organic beef, an obvious alternative to regular beef in terms of safety, both immediately and at a longer term after the BSE crisis. It is based on two random telephone surveys in an Italian region, the first one conducted in 2001 (few months after the BSE crisis) and the second one in 2003. The analysis is based on an innovative methodology of contingent valuation, keeping into account the possibility for consumers to decide the quantity of their purchase when a price is proposed. The results show that though the effect of the BSE crisis weakened along with time distance, it left some permanent signs in consumers’ behaviour. The main conclusion is that the demand for organic beef reduced, but that in the meantime it became more inelastic.BSE, organic beef, willingness to pay, contingent valuation