M ay 2 00 3 q Statistics on S n and Pattern Avoidance
نویسنده
چکیده
Natural q analogues of classical statistics on the symmetric groups Sn are introduced; parameters like: the q-length, the q-inversion number, the q-descent number and the q-major index. MacMahon’s theorem about the equi-distribution of the inversion number and the reverse major index is generalized to all positive integers q. It is also shown that the q-inversion number and the q-reverse major index are equidistributed over subsets of permutations avoiding certain patterns. Natural q analogues of the Bell and the Stirling numbers are related to these q statistics through the counting of the above pattern-avoiding permutations. Partially supported by Minerva Grant No. 8441 and by EC’s IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272 Partially supported by EC’s IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272
منابع مشابه
. A P ] 8 M ay 2 00 6 LOW - REGULARITY SCHRÖDINGER MAPS , II : GLOBAL WELL - POSEDNESS IN DIMENSIONS d ≥ 3
In dimensions d ≥ 3, we prove that the Schrödinger map initialvalue problem { ∂ts = s×∆xs on R × R; s(0) = s0 is globally well-posed for small data s0 in the critical Besov spaces Ḃ d/2 Q (R ; S), Q ∈ S.
متن کاملar X iv : m at h / 01 05 23 2 v 1 [ m at h . N T ] 2 8 M ay 2 00 1 MODULAR CURVES OF GENUS 2
We prove that there are exactly 149 genus two curves C defined over Q such that there exists a nonconstant morphism π : X 1 (N) → C defined over Q and the jacobian of C is Q-isogenous to the abelian variety A f attached by Shimura to a newform f ∈ S 2 (Γ 1 (N)). We determine the corresponding newforms and present equations for all these curves.
متن کامل2 v 2 2 7 M ay 2 00 7 Structure of Light Scalar Mesons from D s and D 0 Non - Leptonic Decays
Non-leptonic D meson decays may provide a reliable testbed for the multiquark interpretation of light scalar mesons. In this letter we consider D s decay and show that a 4-quark f 0 (980) meson could induce a decay pattern, which is forbidden for a q ¯ q constituent structure. Experimental tests to probe such possibilities are within reach in the near future.
متن کاملm at h . Q A ] 3 1 M ay 2 00 0 SO ( 3 ) invariants of Seifert manifolds and their algebraic integrality ∗
For Seifert manifold M = X(p1/q1 , p2/q2 , · · · , pn/qn), τ ′ r(M) is calculated for all r odd ≥ 3. If r is coprime to at least n − 2 of pk (e.g. when M is the Poincare homology sphere), it is proved that ( √
متن کامل6 M ay 2 00 3 Power law distribution of Rényi entropy for equilibrium systems having nonadditive energy
Using Rényi entropy, an alternative thermo-statistics to Tsallis one for nonextensive systems at equilibrium is discussed. We show that it is possible to have the q-exponential distribution function for equilibrium nonextensive systems having nonadditive energy but additive entropy. It is also shown that additive energy makes no sense and is not suitable for interacting systems described by non...
متن کامل