We formulate a series of conjectures (and a few theorems) on the quotient of the polynomial ring Q[Z1 xn, y1,.. . , yn] in two sets of variables by the ideal generated by all Sn invariant polynomials without constant term. The theory of the corresponding ring in a single set of variables X = { x 1 , . . . , xn} is classical. Introducing the second set of variables leads to a ring about which li...

We give a characteristic-free proof that general codimension-1 Schubert varieties meet transversally in a Grassmannian and in some related varieties. Thus the corresponding intersection numbers computed in the Chow (and quantum Chow) rings of these varieties are enumerative in all characteristics. We show that known transversality results do not apply to these enumerative problems, emphasizing ...

When numbers are added in the usual way carries occur along the route. These carries cause a mess and it is natural to seek ways to minimize them. This paper proves that balanced arithmetic minimizes the proportion of carries. It also positions carries as cocycles in group theory and shows that if coset representatives for a finite-index normal subgroup H in a group G can be chosen so that the ...

The aim of the paper is to give a preliminary overview of some of the results of the thesis prepared by the author. We propose a bijective classification of the subgroups of the modular group by pointed trivalent diagrams. Conjugacy classes of those subgroups are in one to one correspondence with unpointed trivalent diagrams. We also give in the form of generating series, the number of those tr...

Using various results from extremal set theory (interpreted in the language of additive combinatorics), we prove an asyptotically sharp version of Freiman’s theorem in Fn2 : if A ⊆ Fn2 is a set for which |A + A| 6 K|A| then A is contained in a subspace of size 2 √ K log K)|A|; except for the O( √ K logK) error, this is best possible. If in addition we assume that A is a downset, then we can als...

The paper deals with the study of the spatial distribution and the design of sampling plans for estimating nymph densities of the grape leafhopper Scaphoideus titanus Ball in vine plant canopies. In a reference vineyard sampled for model parameterization, leaf samples were repeatedly taken according to a multistage, stratified, random sampling procedure, and data were subjected to an ANOVA. The...