arXiv subjects

Pavle Blagojević

Publications and source records attributed to Pavle Blagojević.

3 recordsLinked to original sources

arXiv2012

The Schwarz genus of the Stiefel manifold and counting geometric configurations

In this paper we compute: the Schwarz genus of the Stiefel manifold $V_k(\mathbb R^n)$ with respect to the action of the Weyl group $W_k:=(\mathbb Z/2)^{k}\rtimesΣ_k$, and the Lusternik--Schnirelmann category of the quotient space $V_k(\mathbb R^n)/W_k$. Furthermore, these results are used in estimating the number of: critically outscribed parallelotopes around the strictly convex body, and Birkhoff--James orthogonal bases of the normed finite dimensional vector space.

math.AT↗

arXiv2012

Turán numbers for $K_{s,t}$-free graphs: topological obstructions and algebraic constructions

We show that every hypersurface in $\R^s\times \R^s$ contains a large grid, i.e., the set of the form $S\times T$, with $S,T\subset \R^s$. We use this to deduce that the known constructions of extremal $K_{2,2}$-free and $K_{3,3}$-free graphs cannot be generalized to a similar construction of $K_{s,s}$-free graphs for any $s\geq 4$. We also give new constructions of extremal $K_{s,t}$-free graphs for large $t$.

math.CO↗

arXiv2012

Extensions of theorems of Rattray and Makeev

We consider extensions of the Rattray theorem and two Makeev's theorems, showing that they hold for several maps, measures, or functions simultaneously, when we consider orthonormal $k$-frames in $\R^n$ instead of orthonormal basis (full frames). We also present new results on simultaneous partition of several measures into parts by $k$ mutually orthogonal hyperplanes. In the case $k=2$ we relate the Rattray and Makeev type results with the well known embedding problem for projective spaces.

math.AT↗