Refined Dual Stable Grothendieck Polynomials and Generalized Bender-Knuth Involutions

ar X iv : m at h / 02 06 16 9 v 1 [ m at h . C O ] 1 7 Ju n 20 02 SOME STATISTICS ON RESTRICTED 132 INVOLUTIONS

In [GM] Guibert and Mansour studied involutions on n letters avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary pattern on k letters. They also established a bijection between 132-avoiding involutions and Dyck word prefixes of same length. Extending this bijection to bilateral words allows to determine more parameters; in particular, we consider the...

Notes on Schubert, Grothendieck and Key Polynomials

We introduce common generalization of (double) Schubert, Grothendieck, Demazure, dual and stable Grothendieck polynomials, and Di Francesco–Zinn-Justin polynomials. Our approach is based on the study of algebraic and combinatorial properties of the reduced rectangular plactic algebra and associated Cauchy kernels.

Shifted K-theoretic Poirier-reutenauer Algebra

Poirier and Reutenauer defined a Hopf algebra on the Z-span of all standard Young tableaux in [10], which is later studied in [4, 11]. The Robinson-Schensted-Knuth insertion was used to relate the bialgebra to Schur functions. Schur function is a class of symmetric functions that can be determined by the summation of all semistandard Young tableaux of shape . With the help of the PR-bialgebra, ...

Topological rigidity and H1–negative involutions on tori

Ring-like Structures Derived from Λ-lattices with Antitone Involutions

Using the concept of the λ-lattice introduced recently by V. Snášel we define λ-lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.