A probabilistic approach to some of Euler’s number theoretic identities

DOI10.1090/S0002-9947-98-01969-2zbMath0902.60092MaRDI QIDQ4211084

Don Rawlings

Publication date: 10 September 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Bernoulli trials\(q\)-binomial theorem\(q\)-Riemann zeta function\(q\)-derangement problem\(q\)-Poisson distribution\(q\)-Euler phi functionEuler's partition identitiesEuler's process

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Combinatorial aspects of partitions of integers (05A17) Special processes (60K99) Elementary theory of partitions (11P81)

Related Items (4)

A generalized Mahonian statistic on absorption ring mappings ⋮ \(q\)-deformations of statistical mechanical systems and motives over finite fields ⋮ Absorption processes: Models for \(q\)-identities ⋮ Elementary divisors and determinants of random matrices over a local field.

Cites Work

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• Absorption processes: Models for \(q\)-identities
• A combinatorial interpretation of q-derangement and q-Laguerre numbers
• Counting permutations with given cycle structure and descent set
• A Probabilistic Proof of Ramanujan’s ${}_1 \psi _1 $ Sum
• A Coin-Tossing Problem and Some Related Combinatorics
• Oil exploration: sequential decisions in the face of uncertainty
• On q-Derangement Numbers
• Bernoulli Trials and Mahonian Statistics: A Tale of Two q's
• Bernoulli Trials and Number Theory

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