Euler's partition theorem and the combinatorics of -sequences

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Question: What is the generating function for truncated l-lecture hall partitions? Question: What is the right q-analog of the l-nomial (and the right interpretation) to explain and generalize lecture hall partitions? (We know what lecture hall partitions look like in the “l-world”. What about ordinary partitions? partitions into distinct parts?) Question: There are several q-series identities related to Euler’s theorem, such as Lebesgue’s identity the Roger’s-Fine identity Cauchy’s identity Are there l-analogs?
Sincere thanks to ... You, the audience The FPSAC08 Organizing Committee The FPSAC08 Program Committee Luc Lapointe
Page 1 and 2:
Euler’s partition theorem and the
Page 3 and 4:
Overview Euler’s partition theore
Page 5 and 6:
Overview 1, 2, 3, . . . l-sequences
Page 7 and 8:
Overview 1, 2, 3, . . . l-sequences
Page 9 and 10:
Sylvester’s Bijection
Page 11 and 12:
l-sequences For integer l ≥ 2, de
Page 13 and 14: l-sequences For integer l ≥ 2, de
Page 15 and 16: l = 2 The l-Euler theorem [BME2]: T
Page 17 and 18: l = 3 The l-Euler theorem [BME2]: T
Page 19: The insertion step To insert a k +
Page 22 and 23: Binary numeration system 1 0 1 1 0
Page 24 and 25: Binary numeration system 1 0 1 1 0
Page 26: Theorem [Fraenkel 1985] Every nonne
Page 31 and 32: Lecture Hall Partitions
Page 33 and 34: The Lecture Hall Theorem [BME1] The
Page 35 and 36: Θ (l) n : Bijection for the l-Lect
Page 44 and 45: Truncated lecture hall partitions L
Page 46 and 47: Theorem [Corteel,S 2004] Given posi
Page 48 and 49: The l-nomial coefficient Example (
Page 50 and 51: Let u l and v l be the roots of the
Page 52 and 53: Let u l and v l be the roots of the
Page 54 and 55: An l-nomial theorem [LS]: An analog
Page 56 and 57: A coin-flipping interpretation of t
Page 58 and 59: Define a q-analog of the l-nomial:
Page 60 and 61: Another q-analog of the l-nomial Le
Page 62 and 63: Question: When l = 2, several refin
Page 66 and 67: CanaDAM 2009 2nd Canadian Discrete
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Euler's partition theorem and the combinatorics of -sequences

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