Bijective combinatorics of positive braids
نویسندگان
چکیده
منابع مشابه
Bijective combinatorics of positive braids
We give a new and bijective proof for the formula of the growth function of the positive braid monoid with respect to Artin generators.
متن کاملBijective Combinatorics of Reduced Decompositions
We study the bijective combinatorics of reduced words. These are fundamental objects in the study of Coxeter groups. We restrict our focus to reduced words of permutations and signed permutations. Our results can all be situated within the context of two parallels. The first parallel is between the enumerative theory of reduced words and that of Coxeter group elements. The second parallel is be...
متن کاملCombinatorics of normal sequences of braids
Many natural counting problems arise in connection with the normal form of braids—and seem to have not been much considered so far. Here we solve some of them. One of the noteworthy points is that a number of different induction schemes appear. The key technical ingredient is an analysis of the normality condition in terms of permutations and their descents, in the vein of the Solomon algebra. ...
متن کاملLinking Clifford Analysis and Combinatorics through Bijective Methods
The application of Clifford Analysis methods in Combinatorics has some peculiarities due to the use of noncommutative algebras. But it seems natural to expect from here some new results different from those obtained by using approaches based on several complex variable. For instances, the fact that in Clifford Analysis the point-wise multiplication of monogenic functions as well as their compos...
متن کاملLong games on positive braids
We introduce two games played on positive braids. The first game is played on 3-strand positive braids and its termination time is Ackermannian in the input. We give an ordinal-theoretic and a model-theoretic proof (using semi-regular cuts in models of arithmetic). The second game is played on arbitrary positive braids and its termination is unprovable in IΣ2, the two-quantifier induction arith...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2007
ISSN: 1571-0653
DOI: 10.1016/j.endm.2007.07.038