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Tesi etd-01182016-121436


Thesis type
Tesi di laurea magistrale
Author
CODENOTTI, GIULIA
URN
etd-01182016-121436
Title
Relative Kruskal-Katona theorem
Struttura
MATEMATICA
Corso di studi
MATEMATICA
Commissione
relatore Prof. Sanyal, Raman
correlatore Prof. Dvornicich, Roberto
Parole chiave
  • relative multicomplexes
  • Macaulay Theorem
  • Kruskal-Katona Theorem
  • f-vectors
  • relative simplicial complexes
Data inizio appello
05/02/2016;
Consultabilità
completa
Riassunto analitico
The focus of this work is studying f-vectors in a relative setting. The Kruskal-Katona theorem is a fundamental theorem in Combinatorics which characterizes f-vectors of simplicial complexes. A similar theorem for multicomplexes is the Macauley theorem, which also has a very natural formulation in terms of Hilbert functions of standard graded K-algebras. In my thesis I consider the question of characterizing f-vectors of relative simplicial complexes. A relative simplicial complex is a collection of sets given as the set-theoretic difference between a simplicial complex and a subcomplex. I obtain combinatorial and algebraic generalizations of the Kruskal-Katona and Macaulay characterizations under certain conditions on the number of vertices of simplicial complexes constituting the relative complex.
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