Geodesic
A Convolution Formula for Tutte Polynomials of Arithmetic Matroids and Other Combinatorial Structures
Séminaire lotharingien de combinatoire, 78B (2017)

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We generalize the convolution formula for the Tutte polynomial of Kook-Reiner-Stanton and Etienne-Las Vergnas to a more general setting that includes both arithmetic matroids and delta-matroids. As corollaries, we obtain new proofs of two positivity results for pseudo-arithmetic matroids and a combinatorial interpretation of the arithmetic Tutte polynomial at infinitely many points in terms of arithmetic flows and colorings. We also exhibit connections with a decomposition of Dahmen-Micchelli spaces and lattice point counting in zonotopes. Subsequently, we investigate the following problem: given a representable arithmetic matroid, when is the arithmetic matroid obtained by taking the kth power of its multiplicity function again representable? Bajo-Burdick-Chmutov have recently discovered that Arithmetic matroids of this type arise in the study of CW complexes. We also solve a related problem for the Grassmannian. 

@article{SLC_2017_78B_a3,
     author = {Spencer Backman and Matthias Lenz},
     title = {A {Convolution} {Formula} for {Tutte} {Polynomials} of {Arithmetic} {Matroids} and {Other} {Combinatorial} {Structures}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a3/}
}
TY  - JOUR
AU  - Spencer Backman
AU  - Matthias Lenz
TI  - A Convolution Formula for Tutte Polynomials of Arithmetic Matroids and Other Combinatorial Structures
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a3/
ID  - SLC_2017_78B_a3
ER  - 
%0 Journal Article
%A Spencer Backman
%A Matthias Lenz
%T A Convolution Formula for Tutte Polynomials of Arithmetic Matroids and Other Combinatorial Structures
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a3/
%F SLC_2017_78B_a3
Spencer Backman; Matthias Lenz. A Convolution Formula for Tutte Polynomials of Arithmetic Matroids and Other Combinatorial Structures. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a3/