fall 2026

math 372 · combinatorics

Algebraic and analytic combinatorics — counting with matrices and power series.

syllabus: Syllabus
meetings: MWF 9–9:50 in Eliot 207
office hours: Drop-in: MW 1:00–2:30 in Library 306
By appointment: F 1:00–3:00 in Library 306
scheduling: Book a 20-minute slot⋄or email ormsbyk@reed.edu if none of these times work
forms: Extension request
texts: Stanley, Algebraic Combinatorics⋄Flajolet & Sedgewick, Analytic Combinatorics
discussion: Zulip workspace
submissions: Gradescope

The schedule below is provisional and will be updated as the term proceeds. Readings should be done before the meeting they are listed under.

jump to this week ↓39 meetings

week 1

mon aug 31

Course architecture: matrices and power series, the two languages
readingStanley §1
linksdemo

wed sep 2

The spectral theorem does combinatorics: $tr A^{n} = \sum_{i} λ_{i}^{n}$
readingStanley §1
noteanonymous AI survey

fri sep 4

Worked spectra: $K_{n}$ , cycles, and the cube
readingStanley §1
assignedproblem set due September 11

week 2

mon sep 7break

Labor Day — no class ☭

wed sep 9

Cubes and the Radon transform I
readingStanley §2

fri sep 11

Cubes and the Radon transform II: the spectrum of $Q_{n}$
readingStanley §2
linksgraph spectra
dueproblem set by 10pm

week 3

mon sep 14

Random walks on graphs
readingStanley §3
linksrandom walk demo
assignedlab due September 28

wed sep 16

Posets, rank symmetry, and the Sperner property
readingStanley §4
assignedproblem set due September 25

fri sep 18

Order-raising operators and the linear algebra method
readingStanley §4
linksSperner chains

week 4

mon sep 21

The Sperner property for $B_{n}$ ; contrast with Dilworth
readingStanley §4

wed sep 23

Group actions on Boolean algebras
readingStanley §5

fri sep 25

Quotient posets $B_{n} / G$
readingStanley §5
dueproblem set by 10pm

week 5

mon sep 28

The Sperner property for quotients
readingStanley §5
duelab by 10pm
noteproject menu released

wed sep 30

The Matrix-Tree Theorem: Laplacians and the statement
readingStanley §9
noteboard presentations

fri oct 2

Matrix-Tree via Cauchy–Binet
readingStanley §9

week 6

mon oct 5

Cayley's formula; spanning trees of $K_{n}$ and $Q_{n}$
readingStanley §9
noteboard presentations

wed oct 7

Act I synthesis: it was all a rank computation

fri oct 9

Combinatorial classes, size, and ordinary generating functions
readingFS I.1
noteproblem set 3 due by 10pm

week 7

mon oct 12

The admissible constructions: sum, product, sequence
readingFS I.2

wed oct 14

Integer partitions; specification to generating function as an algorithm
readingFS I.3
noteproject pitches (four students)

fri oct 16

Young diagrams and $q$ -binomial coefficients I
readingStanley §6
noteproject proposal due⋄project pitches (three students)

fall break

October 17-25break

Fall break 🍂

week 8

mon oct 26

$q$ -binomials II: unimodality, and the Sperner callback
readingStanley §6
noteboard presentation

wed oct 28

Words and regular languages: the seed of the transfer matrix
readingFS I.4

fri oct 30

Tree structures and the Catalan numbers
readingFS I.5
noteproblem set 4 due by 10pm

week 9

mon nov 2

Labelled classes, exponential generating functions, the labelled product
readingFS II.1–II.2
noteboard presentations

wed nov 4

Surjections, set partitions, permutations; the exp–log pattern
readingFS II.3–II.4
notecomputational lab 2 assigned

fri nov 6

Pólya theory as the multiset construction: the cycle index
readingStanley §7⋄FS I.6
noteannotated bibliography and computation prospectus due

week 10

mon nov 9

Transfer matrices: Act I and Act II are the same theorem
readingFS V.5–V.6

wed nov 11

Partial fractions and exact asymptotics: poles are reciprocal eigenvalues
readingFS IV.5

fri nov 13

Perron–Frobenius, growth constants, and supercritical sequences
readingFS V.2
noteproblem set 5 due by 10pm

week 11

mon nov 16

Complex differentiability; generating functions as analytic objects
readingFS IV.1–IV.2
noteindividual project meetings this week

wed nov 18

Contour integration and Cauchy's integral formula
readingFS IV.2
noteproblem set 6 due by 10pm

fri nov 20

Residues and the exponential growth formula
readingFS IV.3
notecomputational lab 2 due

week 12

mon nov 23

Catch-up and worked examples

wed nov 25

The standard scale $(1 - z)^{- α}$ : singularity analysis and transfer
readingFS VI.1–VI.4

fri nov 27break

Thanksgiving — no class

week 13

mon nov 30

Singularity analysis in practice: the process and multiple singularities
readingFS VI.4–VI.5

wed dec 2

Simple varieties of trees: the square-root singularity and the universal $n^{- 3/2}$
readingFS VII.3
notefull project draft distributed for peer review

fri dec 4review

Problem session: singularity analysis at the board

week 14

mon dec 7

Course synthesis: the completed dictionary, end to end
notepeer reviews due

wed dec 9

The edge: meanders, growth constants, and what is not known
readingFS VII.7–VII.8
notefinal paper due Friday, December 11 by 10pm

finals week

December 14-17final

MATH 372 Symposium
notefifteen-minute talks⋄time and room to be scheduled by the registrar