Euler's partition theorem and the combinatorics of -sequences

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Inspiration BME1 Mireille Bousquet-Mélou, and Kimmo Eriksson, Lecture hall partitions, Ramanujan. J., 1:1, 1997, 101-111. BME2 Mireille Bousquet-Mélou, and Kimmo Eriksson, Lecture hall partitions II, Ramanujan. J., 1:2, 1997, 165-185. Reference SY07 C. D. S. and Ae Ja Yee, Euler’s partition theorem and the combinatorics of l-sequences, JCTA, 2007, to appear, available online. LS08 Nicholas Loehr, and C. D. S. Notes on l-nomials, in preparation.
Overview Euler’s partition theorem
Page 1: Euler’s partition theorem and the
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 64 and 65:
Question: What is the generating fu
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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