We generalize the notion of graded posets to what we call sign-graded (labeled) posets. We prove that the W -polynomial of a sign-graded poset is symmetric and unimodal. This extends a recent result of Reiner and Welker who proved it for graded posets by associating a simplicial polytopal sphere to each graded poset. By proving that the W -polynomials of sign-graded posets has the right sign at...

An exposition of the different definitions and approaches to quantum statistics is given, with emphasis in one-dimensional situations. Permutation statistics, scattering statistics and exclusion statistics are analyzed. The Calogero model, matrix model and spin chain models constitute specific realizations. E-mail: [email protected]

Using a recent construction of Bezrukavnikov and Etingof, [BE], we prove that there is a factorization of the Etingof-Ginzburg sheaf on the generalized Calogero-Moser space associated to a complex reflection group. In the case W = Sn, this confirms a conjecture of Etingof and Ginzburg, [EG].

We compute the r-matrix for the elliptic Euler-Calogero-Moser model. In the trigonometric limit we show that the model possesses an exact Yangian symmetry. PAR LPTHE 94-03 L.P.T.H.E. Université Paris VI (CNRS UA 280), Box 126, Tour 16, 1er étage, 4 place Jussieu, F-75252 PARIS CEDEX 05

A semigroup S is called surjective if S 2 = S. The aim of this paper is to prove that p n-sequences of nite surjective semigroups are eventually strictly increasing, except in few well known cases, when they are bounded. Also, some further types of nite semigroups, obtained by means of subdirect products, are shown to have the same property.

For an undirected graph G, a zero-sum flow is an assignment of non-zero real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero. It has been conjectured that if a graph G has a zero-sum flow, then it has a zero-sum 6-flow. We prove this conjecture and Bouchet’s Conjecture for bidirected graphs are equivalent. Among other results it is shown that...

As the chapters in this volume attest, the foundational premise that culture and person coconstitute one another, perhaps more than any other, characterizes contemporary cultural psychology (Cole, 1996; Kitayama, 2002; Miller, 1997; 1999; Piker, 1998; Shweder, 1990). Ironically, however, this very premise is most challenging for a cultural psychological view of personality, for “personality” ha...

Visualizing permutations as labelled trees allows us to to specify restricted permutations, and to analyze their counting sequence. The asymptotic behaviour for permutations that avoid a given pattern is given by the Stanley-Wilf conjecture, which was proved by Marcus and Tardos in 2005. Another interesting question is the occurence of generalized patterns, i.e. patterns containing subwords. Th...

We apply the Painlevé test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess infinitely many commuting local generalized symmetries without any recursion operator. The Painlevé analysis easily detects that this is a typical C-integrable system in the Calogero sense and rediscov...