A bstract We develop a method of transverse momentum dependent (TMD) operator expansion that yields the TMD factorization theorem on level. The operators are systematically ordered with respect to TMD-twist, which allows certain separation kinematic and genuine power corrections. process dependence enters via boundary conditions for background fields. As proof principle, we derive effective had...

Let k and p be positive integers and let Q be a finite point set in general position in the plane. We say that Q is (k, p)-Ramsey if there is a finite point set P such that for every k-coloring c of ( P p ) there is a subset Q′ of P such that Q′ and Q have the same order type and ( Q′ p ) is monochromatic in c. Nešetřil and Valtr proved that for every k ∈ N, all point sets are (k, 1)-Ramsey. Th...

This paper presents symmetry classes of the Hartree-Fock (HF) solutions of spin and orbital ordered states in a t2g Hubbard model on a two-dimensional square lattice. Using a group theoretical bifurcation theory of the Hartree-Fock equation, we obtained many types of broken symmetry solutions which bifurcate from the normal state through one step transition in cases of commensurate ordering vec...

We prove that the class of permutations generated by passing an ordered sequence 12 . . . n through a stack of depth 2 and an infinite stack in series is in bijection with an unambiguous context-free language, where a permutation of length n is encoded by a string of length 3n. It follows that the sequence counting the number of permutations of each length has an algebraic generating function. ...

In this paper we answer Open Problem 2 of Goodearl’s book on partially ordered abelian groups in the case of partially ordered simple groups. As a consequence, we obtain a version of the Theorem of structure of dimension groups in the case of simple Riesz groups. Also, we give a method for constructing torsion-free strictly perforated simple Riesz groups of rank one, and we see that every dense...

In a monotonic sequence game, two players alternately choose elements of a sequence from some fixed ordered set. The game ends when the resulting sequence contains either an ascending subsequence of length a or a descending one of length d. We investigate the behaviour of this game when played on finite linear orders or Q and provide some general observations for play on arbitrary ordered sets.

An ordered partition of [n] := {1, 2, . . . , n} is a sequence of disjoint and nonempty subsets, called blocks, whose union is [n]. The aim of this paper is to compute some generating functions of ordered partitions by the transfer-matrix method. In particular, we prove several conjectures of Steingrı́msson, which assert that the generating function of some statistics of ordered partitions give ...

Let P be an ordered set. P is said to have the finite cutset property if for every x in P there is a finite set F of elements which are noncomparable to x such that every maximal chain in P meets {x} t.J F. It is well known that this property is equivalent to the space of maximal chains of P being compact. We consider the following question: Which ordered sets P can be embedded in an ordered se...

Schur Q-functions were originally introduced by Schur in relation to projective representations of the symmetric group and they can be defined combinatorially in terms of shifted tableaux. In this paper we describe planar decompositions of shifted tableaux into strips and use the shapes of these strips to generate pfaffi.ans and determinants that are equal to Schur Q-functions. As special cases...

In a monotonic sequence game, two players alternately choose elements of a sequence from some fixed ordered set. The game ends when the resulting sequence contains either an ascending subsequence of length a or a descending one of length d. We investigate the behaviour of this game when played on finite linear orders or Q and provide some general observations for play on arbitrary ordered sets.