J. Propp

activity

19982004

most citedThe many faces of alternating-sign matrices

2 citations · 2 across the 3 of their papers we have counts for

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13 papers · 1 filter

math.CO2004

Lambda-determinants and domino-tilings

James Propp

Consider the $2 n$ -by- $2 n$ matrix $M = (m_{i, j})_{i, j = 1}^{2 n}$ with $m_{i, j} = 1$ for $i, j$ satisfying $∣2 i - 2 n - 1∣ + ∣2 j - 2 n - 1∣ \leq 2 n$ and $m_{i, j} = 0$ for all other $i, j$ , consisting…

math.CO2002★ 2 cited

The many faces of alternating-sign matrices

James Propp

I give a survey of different combinatorial forms of alternating-sign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrice…

math.CO2002

Euler measure as generalized cardinality

James Propp

Schanuel has pointed out that there are mathematically interesting categories whose relationship to the ring of integers is analogous to the relationship between the category of fi…

math.CO2002

Exponentiation and Euler measure

James Propp

Two of the pillars of combinatorics are the notion of choosing an arbitrary subset of a set with $n$ elements (which can be done in $2^{n}$ ways), and the notion of choosing a $k$ -el…

math.CO2001

Generalized domino-shuffling

James Propp

The problem of counting tilings of a plane region using specified tiles can often be recast as the problem of counting (perfect) matchings of some subgraph of an Aztec diamond grap…

math.CO2001

A reciprocity theorem for domino tilings

James Propp

Let T(m,n) denote the number of ways to tile an m-by-n rectangle with dominos. For any fixed m, the numbers T(m,n) satisfy a linear recurrence relation, and so may be extrapolated…