Lec 1, 8/24 Mon, Sec 11.1:
Course overview, Dilworth's Theorem, Gallai-Milgram Theorem.

Lec 2, 8/26 Wed, Sec 11.1:
saturated chain partitions, set-up for Greene-Kleitman Theorem.

Lec 3, 8/28 Fri, Sec 11.1:
proof of Greene-Kleitman Theorem, skipped polyunsaturated posets.

Lec 4, 8/31 Mon, Sec 11.1-2:
*k*-cofamilies, Berge optimal path partitions, semiantichain conjecture,
LYM Inequality, reminder of characterization of LYM orders, partition lattice.

Lec 5, 9/02 Wed, Sec 11.2:
weighted LYM inequality and strong Sperner property, LYM for products,
Bollobas generalization of LYM, application to disjoint chains of subsets

Lec 6, 9/04 Fri, Sec 11.3:
Symmetric chain orders (products), bracketing for multisets, reminder of
counting monotone Boolean functions, orthogonal chain decompositions with
probability application, (skipped) 2-part Sperner property, open problem
for *M(n)*.

Lec 7, 9/09 Wed, Sec 11.3:
symmetric chains for *L(3,n)*, comment on symmetric chains for LYM orders,
strong Hall condition.

Lec 8, 9/11 Fri, Sec 11.3-11.4:
symmetric chains for locally self-dual posets,
examples of lattices, sublattices, elementary lattice properties.

Lec 9, 9/14 Mon, Sec 11.4:
Distributive lattices, characterization by join-irreducibles.

Lec 10, 9/16 Wed, Sec 11.4:
Characterizations of distributive and modular lattices.

Lec 11, 9/18 Fri, Sec 11.5:
Comparability graphs (G-H Theorem).

Lec 12, 9/21 Mon, Sec 11.5:
Edge-classes and knotting graph, incomparability graphs and *k*-asteroids,
modular decomposition tree, (cover graphs skipped).

Lec 13, 9/23 Wed, Sec 12.1:
Rankings, voting paradoxes, Arrow's Theorem, median rankings.

Lec 14, 9/25 Fri, Sec 12.1:
Characterization of semiorders, interval orders, and Ferrers digraphs
(biorders).

Lec 15, 9/28 Mon, Sec 12.2:
Dimension of posets (examples, characterizations, 2-dimensional posets)
Alternating cycles, unforced pairs

Lec 16, 9/30 Wed, Sec 12.2:
one-point removal, Hiraguchi theorems, four-point removal.

Lec 17, 10/2 Fri, Sec 12.2:
Dimension of products, compositions, semiorders, interval orders;
interval dimension.

Lec 18, 10/5 Mon, Sec 12.3:
Dimension of generalized crowns, bipartite posets (suitable sets),
*d _{n}(1,k)* (Dushnik's Theorem).

Lec 19, 10/7 Wed, Sec 12.3: Furedi-Kahn bound for

Lec 20, 10/9 Fri, Sec 12.3: Four-problem answer (lg lg n + (1/2) lg lg lg n), shift graph and double shift graph, dimension of planar posets (very brief mention only).

Lec 21, 10/12 Mon, Sec 12.3-4:
Containment posets (circle orders, angle orders), Alon-Scheinerman Theorem),
correlation (Chebyshev's Inequality)

Lec 22, 10/14 Wed, Sec 12.4:
Kleitman's Inequality, FKG Inequality, Four Function Inequality.

Lec 23, 10/16 Fri, Sec 12.4:
XYZ Inequality, expected height.

Lec 24, 10/19 Mon, Sec 12.5:
δ-balanced comparisons (Linial for width 2, idea of Kahn-Linial for
general width), Aigner on second largest element (details on Aigner and idea
of poset searching postponed to next lecture.)

Lec 25, 10/21 Wed, Sec 13.1:
intersecting families, Erdos-Ko-Rado Theorem for t=1 and Bollobas extension,
general Erdos-Ko-Rado Theorem (sketch).

Lec 26, 10/23 Fri, Sec 13.1:
colex ordering and Kruskal-Katona Theorem, cross-intersecting families
(details and mention of S-intersecting families postponed,
RayChaudhuri-Wilson Theorem skipped).

Lec 27, 10/26 Mon, Sec 13.1:
Berge Lemma for partitioning ideals, Chvatal's Conjecture (Snevily's Theorem),

Lec 28, 10/28 Wed, Sec 13.2:
on-line antichain partitioning (algorithm & lower bound),
on-line chain partitioning (width 2 algorithm, sketch for larger width
postponed).

Lec 29, 10/30 Fri, Sec 13.2:
(was postponed to after next two lectures)
on-line chain partitioning (width 2 lower bd, comment on interval orders)
[continued with cutsets/fibres]

Lec 30, 11/2 Mon, Sec 13.3:
linear discrepancy (bounds for interval orders, width 2, chain products)

Lec 31, 11/4 Wed, Sec 13.3:
linear discrepancy (arbitary extension, product of two chains),
cutsets/fibres (examples, antichain hypergraph is 3-colorable), width of cutset
in subset lattice (brief mention)

Lec 32, 11/6 Fri, Sec 15.1:
Hereditary systems, matroid examples, basic axiomatics (augmentation, exchange,
absorption, uniformity)

Lec 33, 11/9 Mon, Sec 15.1:
Matroid axiomatics (submodularity, elimination, dual base exchange, greedy
algorithm)

Lec 34, 11/11 Wed, Sec 15.1:
span function of hereditary systems, dual matroids (cocircuits and bonds)

Lec 35, 11/13 Fri, Sec 15.1:
Minors, Whitney's planarity criterion.

Lec 36, 11/16 Mon, Sec 15.2:
Matroid Intersection Theorem, Konig-Egervay and CSDR applications.

Lec 37, 11/18 Wed, Sec 15.2:
Matroid Union Theorem and applications (covering/packing proved, Shannon
switching game stated), skipped Matroid intersection algorithm.

Lec 38, 11/20 Fri, Sec 15.3:
Statement of matroid parity problem (skipped polymatroids and polymatroidal
network flow), Connected matroids (skipped Whitney's 2-Isomorphism Theorem).

Lec 39, 11/30 Mon, Sec 15.3:
Gammoids, Linkage Lemma, duality between Konig and Menger Theorems.

Lec 40, 12/2 Wed, Sec 15.3:
Duals of linear matroids, characterization of binary matroids.

Lec 41, 12/4 Fri, Sec 15.4:
Lattices and matroids (closed sets, geometric, semimodular)

Lec 42, 12/7 Mon, Sec 15.4:
Convexity and antimatroids (convex geometry, shelling, rooted circuits)

Lec 43, 12/9 Wed, Sec 15.4:
Greedoids (languages, branching greedoid, skipped interval properties,
diameter of basis graph)
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