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- Stanislaw Bylka, Adam Idzik, Jan Komar
- Graphs and Combinatorics
- 1999

- Stanislaw Bylka, Adam Idzik, Zsolt Tuza
- Discrete Mathematics
- 1999

- Qamrul H. Ansari, Adam Idzik, Jen-Chih Yao, Juliusz P. Schauder
- 2000

In this paper, we first establish a coincidence theorem under the noncompact settings. Then we derive some fixed point theorems for a family of functions. We apply our fixed point theorem to study nonempty intersection problems for sets with convex sections and obtain a social equilibrium existence theorem. We also introduce a concept of a quasi-variational… (More)

- NONORIENTED PSEUDOMANIFOLDS, Adam Idzik, Konstanty Junosza-Szaniawski, K. Junosza-Szaniawski
- 2007

Sperner lemma type theorems are proved for nonoriented pri-moids and pseudomanifolds. A rank function of a primoid is defined. Applications of these theorems to the geometric simplex are given. Also Knaster– Kuratowski–Mazurkiewicz type theorems on covering of the geometric sim-plex are presented.

- Adam Idzik, Gyula O. H. Katona, Rajiv Vohra
- J. Comb. Theory, Ser. A
- 2001

Suppose that any t members (t2) of a regular family on an n element set have at least k common elements. It is proved that the largest member of the family has at least k 1Ât n 1&1Ât elements. The same holds for balanced families, which is a generalization of the regularity. The estimate is asymptotically sharp.

- Adam Idzik, Konstanty Junosza-Szaniawski
- Discussiones Mathematicae Graph Theory
- 2005

We formulate general boundary conditions for a labelling to assure the existence of a balanced n-simplex in a triangulated polyhedron. Furthermore we prove a Knaster-Kuratowski-Mazurkiewicz type theorem for polyhedrons and generalize some theorems of Ichiishi and Idzik. We also formulate a necessary condition for a continuous function defined on a… (More)

- Adam Idzik, Zsolt Tuza
- Discrete Mathematics
- 2001

- Adam Idzik, Marek Izydorek, Juliusz P. Schauder
- 2008

A generalization of the theorem of Zhong on the product of spheres to multivalued maps is given. We prove also a stronger result of Bourgin–Yang type.

A solid combinatorial theory is presented. The generalized Sperner lemma for chains is derived from the combinatorial Stokes formula. Many other generalizations follow from applications of an n-index of a labelling defined on chains with values in primoids. Primoids appear as the most general structure for which Sperner type theorems can be formulated.… (More)

- Adam Idzik, Konstanty Junosza-Szaniawski
- Discussiones Mathematicae Graph Theory
- 2006

We formulate general boundary conditions for a labelling of vertices of a triangulation of a polyhedron by vectors to assure the existence of a balanced simplex. The condition is not for each vertex separately, but for a set of vertices of each boundary simplex. This allows us to formulate a theorem, which is more general than the Sperner lemma and theorems… (More)