Finding involutions with small support

We show that the proportion of permutations $g$ in $S_n$ or $A_n$ such that $g$ has even order and $g^{|g|/2}$ is an involution with support of cardinality at most $\lceil n^\varepsilon \rceil$ is at least a constant multiple of $\varepsilon$. Using this result, we obtain the same conclusion for elements in a classical group of natural dimension $n$ in odd characteristic that have even order and power up to an involution with $(-1)$-eigenspace of dimension at most $\lceil n^\varepsilon \rceil$ for a linear or unitary group, or $2\lceil \lfloor n/2 \rfloor^\varepsilon \rceil$ for a symplectic or orthogonal group

Finding involutions with small support

We show that the proportion of permutations $g$ in $S_n$ or $A_n$ such that $g$ has even order and $g^{|g|/2}$ is an involution with support of cardinality at most $\lceil n^\varepsilon \rceil$ is at least a constant multiple of $\varepsilon$. Using this result, we obtain the same conclusion for elements in a classical group of natural dimension $n$ in odd characteristic that have even order and power up to an involution with $(-1)$-eigenspace of dimension at most $\lceil n^\varepsilon \rceil$ for a linear or unitary group, or $2\lceil \lfloor n/2 \rfloor^\varepsilon \rceil$ for a symplectic or orthogonal group

From disability to accessible tourism : the problem of market segmentation and the creation of tourism products tailored to the needs of people with disabilities

Turystyka dostępna pozwala osobom niepełnosprawnym na samodzielne, sprawiedliwe i godne funkcjonowanie podczas podróżowania. Jest to możliwe dzięki dostarczeniu im odpowiednich produktów turystycznych, usług i środowiska. Jednakże proces kreowania produktów dla potrzeb osób z dysfunkcjami jest czaso- i kosztochłonny (gdyż wymaga likwidowania barier) i charakteryzuje się swoistymi zasadami. Artykuł prezentuje proces kreowania produktów turystycznych powstających z myślą o osobach niepełnosprawnych, o różnym rodzaju i stopniu schorzenia. Przybliżono również terminologię niepełnosprawności oraz segmentacji rynku turystycznego, który odpowiada na potrzeby osób z dysfunkcjami.Accessible tourism allows people with disabilities to independent, fair and decent functioning while traveling. This is made possible by providing them with dedicated tourism products, services, as well as background. However, the process of creating products tailored to the needs of people with disabilities is both time and money consuming, because it requires breaking down barriers, but above all it is characterized by its own rules. The paper presents the process of creating tourism products for people with disabilities of various type and degree of disability, explains the term of disability and the segmentation of the tourism market, which responds to the needs of people with disabilities

The History of Editing Literary and Theatrical Works of Karol Wojtyła – John Paul II

The article is devoted to the history of the edition of literary and theater works of Karol Wojtyla – John Paul II. Based on the surviving materials in the archives, often unknown facts were presented showing the subsequent phases of discovery of Wojtyła as a poet, playwright, and actor.The article is devoted to the history of the edition of literary and theater works of Karol Wojtyla – John Paul II. Based on the surviving materials in the archives, often unknown facts were presented showing the subsequent phases of discovery of Wojtyła as a poet, playwright, and actor

Memory of the Holocaust from the perspective of a theater historian

In his Polski teatr Zagłady [The Polish Theater of the Holocaust], Grzegorz Niziołek, who starts with theater and specific theatrical performances and who focuses on artistic phenomena, presents problems that go far beyond art. This is a book that should be read by historians, literary scholars, political scientists and cultural experts. Sociologists and psychologists who study social behavior will also find some of its sections interesting. This Cracow theatrologist presents the extermination of Jews during the occupation of Poland as well as Polish-Jewish relations, i.e. one of the most difficult Polish problems, permeated with silence and resentment, in the form of a monograph and in relation to the history of post-war theater, of which it is an important par

Accessible tourism in a knowledge-based economy

Turystyka osób z ograniczoną sprawnością jest fenomenem, który mocno się rozwija. Jednakże pomimo trwającego rozwoju wciąż – w pewnym stopniu – jest zjawiskiem rzadkim. Wynika to przede wszystkim z braku wiedzy na temat rynku turystów ze specjalnymi potrzebami, braku dialogu, koordynacji i wymiany informacji pomiędzy różnymi szczeblami władzy, przedsiębiorstwami branży turystycznej itp., które współdziałają w ramach gospodarki opartej na wiedzy. Artykuł prezentuje przykłady konkurencyjnych i innowacyjnych projektów na rzecz rozwoju turystyki osób niepełnosprawnych. Przybliżona zostaje również terminologia niepełnosprawności oraz segmentacja rynku turystycznego, który odpowiada na potrzeby osób z dysfunkcjami.Tourism for disabled people is a phenomenon that is strongly growing. However, despite its development still – to some extent – is rare. This is mainly due to the lack of knowledge on the market of tourist with special needs, the lack of dialogue, coordination and exchange of information between different levels of government, businesses, tourism industry, etc. that cooperate with each other in a knowledge-based economy. The paper presents examples of competitive and innovative projects for developing accessible tourism, explains the term of disability and the segmentation of the tourism market, which responds to the needs of people with disabilities