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We find the threshold between avoidable and unavoidable repetitions in circular words over k letters for any k 6. Namely, we show that the number CRT(k) = ⌈k/2⌉+1 ⌈k/2⌉ satisfies the following properties. For any n there exists a k-ary circular word of length n containing no repetition of exponent greater than CRT(k). On the other hand, k-ary circular words(More)
As a result of a study of biotas of agaricoid and gasteriod fungi of dryad tundras of the Altai-Sayan mountain area, 80 species of macromycetes were found, 19 of which were found in Southern Siberia for the first time. Species of arctalpine (37.5% of species) and multizonal (22.5% of species) elements; Russullaceae, Cortinariaceae, and Strophariacea(More)
The paper considers the major problems of arid soil formation in the works of M.A. Glazovskaya, including the biogeochemical role of living organisms, soil formation in high-mountain cryo-arid deserts, and the polygenic origin of arid soils, as well as the significance and importance of the assigned tasks for developing soil science and understanding modern(More)
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