Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences Euler's partition theorem and the combinatorics of -sequences
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 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
Sincere thanks to ...<br />
You, <strong>the</strong> audience<br />
The FPSAC08 Organizing Committee<br />
The FPSAC08 Program Committee<br />
Luc Lapointe
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