Category: Combinatorics
Rectangle partitions extend integer partitions
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What the study found The study introduces a geometric extension of the partition function by counting partitions of a rectangle into rectangular blocks with integer sides. Two partitions are treated as the same when they contain the same multiset of blocks, regardless of how the blocks are arranged. Why the authors say this matters The…
Tensor product formulas extend to two graph polynomials
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What the study found The authors define a tensor product for graphs embedded in pseudo-surfaces and use it to generalize and unify several existing tensor product formulas. They provide Brylawski-style formulas for both the Bollobás-Riordan polynomial and the Krushkal polynomial. Why the authors say this matters The study suggests that this framework brings together previously…
New condition for tilings of the symmetric group
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What the study found The authors establish a new necessary condition for when the symmetric group can be tiled by the identity and transpositions, namely that the subset must be partition-transitive with respect to certain partitions. They also study tiling by the set of all transpositions and are led to conjecture that neither of the…
