## 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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