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President TACO
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Proof of a conjecture by Starr and log-concavity for random commuting permutations
Abdelmalek Abdesselam
https://arxiv.org/abs/2506.06894 https://

Proof of a conjecture by Starr and log-concavity for random commuting permutations
We prove a conjecture by Shannon Starr regarding the asymptotics for the number of tuples of commuting permutations with given number of joint orbits. These numbers generalize unsigned Stirling numbers of the first kind which count how many single permutations have a given number of cycles. In the case of pairs of permutations, these numbers are related to D'Arcais polynomials and the Nekrasov-Okounkov formula. As a consequence of the above asymptotics, we confirm a log-concavity conjecture in …

Kilka jeszcze ciekawostek, póki pamiętam - w każdym większym sklepie musi być dział z włóczkami i wszystkim do dziergania. Większość to węłna i liczyliśmy, że gdzieś za 50euro można sobie wydziergać wełniany gruby sweter z szablonu - stąd pewnie tutaj każdy chodzi w wełnie.

Tęczowe flagi są równie częste jak te norweskie - obydwie widać zarówno w domach jak i przed sklepami, w miejscach publicznych czy przed urzędami. Praktycznie od Oslo aż po głęboką prowincje.

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Tyrant from Temu
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Der Derpenführer
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Donorrhea
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Commander in Cheats
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Mendacious Mango
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