1,424 research outputs found
Combinatorial Hopf algebras and Towers of Algebras
Bergeron and Li have introduced a set of axioms which guarantee that the
Grothendieck groups of a tower of algebras can be
endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap,
and independently Lam and Shimozono constructed dual graded graphs from
primitive elements in Hopf algebras. In this paper we apply the composition of
these constructions to towers of algebras. We show that if a tower
gives rise to graded dual Hopf algebras then we must
have where .Comment: 7 page
Tarski's influence on computer science
The influence of Alfred Tarski on computer science was indirect but
significant in a number of directions and was in certain respects fundamental.
Here surveyed is the work of Tarski on the decision procedure for algebra and
geometry, the method of elimination of quantifiers, the semantics of formal
languages, modeltheoretic preservation theorems, and algebraic logic; various
connections of each with computer science are taken up
Perron-Frobenius theory and frequency convergence for reducible substitutions
We prove a general version of the classical Perron-Frobenius convergence
property for reducible matrices. We then apply this result to reducible
substitutions and use it to produce limit frequencies for factors and hence
invariant measures on the associated subshift. The analogous results are well
known for primitive substitutions and have found many applications, but for
reducible substitutions the tools provided here were so far missing from the
theory.Comment: v.2 Minor revisions for submissio
Recommended from our members
Finite Fields: Theory and Applications
Finite fields are the focal point of many interesting geometric, algorithmic and combinatorial problems. The workshop was devoted to progress on these questions, with an eye also on the important applications of finite field techniques in cryptography, error correcting codes, and random number generation
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