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  • Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
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Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {b,c} {a,c} {a,b} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor Gian-Carlo Rota This publication is dedicated to John N. Guidi (1954-2012) whose remarkable almost "verbatim" notes in Prof. Gian-Carlo Rota's courses in 1998 at MIT faithfully reproduce both the content and erudition of Rota's famous lectures just before Rota's premature death in 1999.

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Page 1: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor

Combinatorial Theory

1 = {a,b,c}

{a}

0 = {}

{b} {c}

{b,c}{a,c}{a,b}

John N. Guidi

Lecture Notes – Fall 1998 MIT Course 18.315

Professor Gian-Carlo Rota

This publication is dedicated to John N. Guidi (1954-2012) whose remarkable almost "verbatim" notes in Prof. Gian-Carlo Rota's courses in 1998 at MIT faithfully reproduce both the content and erudition of Rota's famous lectures just before Rota's premature death in 1999.

Page 2: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor

John N. Guidi Research Affiliate Department of Mathematics Room 2-363A Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139 USA Email: [email protected]

Copyright ©2002 John N. Guidi. All rights reserved.

ii

Page 3: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 4: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 5: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 6: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 7: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 8: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 9: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 10: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 11: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 12: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 13: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 14: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 15: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 16: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 17: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 18: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 19: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 20: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 21: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 22: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 23: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 24: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 25: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 26: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 27: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 28: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 29: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 30: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 31: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 32: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 33: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 34: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 35: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 36: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 37: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 38: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 39: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 40: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 41: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 42: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 43: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 44: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 45: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 46: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 47: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 48: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 49: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 50: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 51: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 52: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 53: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 54: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 55: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 56: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 57: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 58: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 59: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 60: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 61: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 62: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 63: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 64: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 65: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 66: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 67: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 68: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 69: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 70: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 71: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 72: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 73: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 74: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
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Page 81: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
Page 82: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
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Page 84: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
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Page 89: Combinatorial Theory - David Ellerman€¦ · Combinatorial Theory 1 = {a,b,c} {a} 0 = {} {b} {c} {a,b} {a,c} {b,c} John N. Guidi Lecture Notes – Fall 1998 MIT Course 18.315 Professor
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