ar X iv : m at h / 06 10 50 5 v 1 [ m at h . Q A ] 1 7 O ct 2 00 6 Tau functions in combinatorial
نویسنده
چکیده
We introduce ultradiscrete tau functions associated with rigged configurations for A (1) n . They satisfy an ultradiscrete version of the Hirota bilinear equation and play a role analogous to a corner transfer matrix for the box-ball system. As an application, we establish a piecewise linear formula for the Kerov-Kirillov-Reshetikhin bijection in the combinatorial Bethe ansatz. They also lead to general N-soliton solutions of the box-ball system.
منابع مشابه
ar X iv : m at h / 06 10 50 5 v 2 [ m at h . Q A ] 1 1 O ct 2 00 7 Tau functions in combinatorial Bethe ansatz
We introduce ultradiscrete tau functions associated with rigged configurations for A (1) n . They satisfy an ultradiscrete version of the Hirota bilinear equation and play a role analogous to a corner transfer matrix for the box-ball system. As an application, we establish a piecewise linear formula for the Kerov-Kirillov-Reshetikhin bijection in the combinatorial Bethe ansatz. They also lead t...
متن کاملar X iv : m at h / 06 10 98 4 v 1 [ m at h . C O ] 3 1 O ct 2 00 6 COLORED POSETS AND COLORED QUASISYMMETRIC FUNCTIONS
The colored quasisymmetric functions, like the classic quasisymmetric functions, are known to form a Hopf algebra with a natural peak subalgebra. We show how these algebras arise as the image of the algebra of colored posets. To effect this approach we introduce colored analogs of P -partitions and enriched P -partitions. We also frame our results in terms of Aguiar, Bergeron, and Sottile’s the...
متن کاملar X iv : m at h / 06 09 42 6 v 3 [ m at h . C O ] 1 5 O ct 2 00 6 SUM - PRODUCT ESTIMATES IN FINITE FIELDS VIA KLOOSTERMAN
We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.
متن کاملar X iv : m at h / 06 10 37 5 v 1 [ m at h . C V ] 1 1 O ct 2 00 6 Classification of Levi degenerate homogeneous CR - manifolds in dimension 5
In this paper we present new examples of homogeneous 2-nondegenerate CRmanifolds of dimension 5 and give, up to local CR-equivalence, a full classification of all CR-manifolds of this type.
متن کاملar X iv : m at h / 06 10 50 1 v 2 [ m at h . G T ] 1 8 O ct 2 00 6 INTRINSIC LINKING IS ARBITRARILY COMPLEX
We prove that given any n, λ ∈ N, there is a graph G which has the property that every embedding of G in R contains an ncomponent link all of whose components are pairwise linked with linking number greater than λ.
متن کامل