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It’s a small world after all, especially when you dance.

African-American slaves created the cakewalk by imitating their strutting plantation owners. Polish villagers invented a form of polka by trying to do what the dance-trained nobility did.

“Of course, the steps didn’t work exactly the same,” said Brygida Linartas, deputy director of Poland’s Mazowsze State Folk Song and Dance Ensemble. “So the dance was changed, and that was the how the tramblanka, over time, came to be.”

The Mazowsze (pronounced mah-ZOFF-shuh) will perform the tramblanka and a slew of other stylized native dances and songs from 38 areas of Poland on Thursday through Saturday at the Cerritos Center for the Performing Arts. The troupe, which travels with a traditional 19-piece band, is known for energetic adaptations of indigenous forms and will present many of its favorites:

* The 18th century mazurka, a vigorous, dignified dance from the region after which the Mazowsze was named.

* A festive shepherd’s dance from the rural Jurgow region. Company members, many of them ballet-trained, will show off their dazzling technical prowess with stunning leaps and the like.

* “Czy Prawda To?” (Is it True?), a song, sung by women, that dispenses Old World wisdom: “Each girl loves only one boy, but all boys are charmers and each of them loves at least two girls.”

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The 49-year-old troupe is also bringing nine new dances on this, its 10th U.S. tour. One, “Tance Opoczynskie,” features the lively tramblanka polka. “Zywiec Mieszczanski” consists of a waltz, a courtly polonaise and a handkerchief dance.

“The girl throws the handkerchief in front of the guy she likes,” Linartas, 51, said recently from a tour stop in Idaho, “and when he picks it up and gives it back to her, she has to pay a kiss.

“Each girl carries a beautiful handkerchief,” she continued through an interpreter. “Each one was handmade by a different family in Zywiec, so the motifs are completely different. No two are the same.”

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Colorful costumes--many embroidered, appliqued or beaded by the country’s leading artisans--are a Mazowsze trademark. The troupe is also known for its performers’ smiles. On-stage joy is a company mandate--which recently faced its greatest challenge.

On Jan. 26, while performing on the East Coast, the company learned that its matriarch had died during the night at age 96.

During World War II--which threatened to annihilate Polish culture--Mira Ziminska-Sygietynska, a noted Polish actress, did research for the Mazowsze with her composer-folklorist husband, Tadeusz Sygietynska, now deceased. Ziminska-Sygietynska remained active with the troupe until recently.

“There was a silence,” recalled Linartas, who had worked with Ziminska-Sygietynska for 30 years. “Then people started to cry so loudly. It was horrible because that day we had a concert in Brooklyn and on the stage, the girls were singing one of the favorite songs, ‘Hush, Hush.’ But you could hear them just crying.”

Linartas, who still dresses in black for mourning, did her best to comfort the dancers. Rushing about backstage, she told them their mentor “is in heaven right now watching you, so be professional. She wants you to have a wonderful performance. It helped, but it was difficult. Of course, they were smiling and crying at the same time.”

* The Mazowsze State Folk Song and Dance Ensemble performs Thursday through Saturday at 8 p.m. at the Cerritos Center for the Performing Arts, 12700 Center Court Drive. $10-$40. (800) 300-4345.