منابع مشابه
Combinatorics of Constructible Complexes
Preface Everything started from one book. I happened to buy the textbook \Lectures on Poly-topes" 98] written by Prof. G unter M. Ziegler, at the university bookstore about ve years ago. I bought it only because the gures (especially of permutahedra and of zonotopal tilings) interested me, but the book turned out to be a very good introduction to the world of poly-topes, starting from fundament...
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Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high-dimensional Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudo-randomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.
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In the first part of this paper (Sections 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12), we introduce and study a simplicial complex ∆(Φ) associated to a finite root system Φ and a nonnegative integer parameter m. For m = 1, our construction specializes to the (simplicial) generalized associahedra ∆(Φ) introduced in [13] and identified in [14] as the underlying complexes for the cluster algebras of f...
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A set of words over a finite alphabet is called an unavoidable set if every word of sufficiently long length must contain some word from this set as a subword. Motivated by a theorem from automata theory, we introduce the notion of an almost unavoidable set and prove certain asymptotic estimates for the size of almost unavoidable sets of uniform length.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2020
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2019.103004