Geodesic
Wiener indices of minuscule lattices
Colin Defant1 ; Valentin Féray2 ; Philippe Nadeau3 ; Nathan Williams4
1MIT
2Institut Elie Cartan de Lorraine, Université de Lorraine
3Institut Camille Jordan, Université Lyon 1
4University of California, Santa Barbara
The electronic journal of combinatorics, Tome 31 (2024) no. 1
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The Wiener index of a finite graph $G$ is the sum over all pairs $(p,q)$ of vertices of $G$ of the distance between $p$ and $q$. When $P$ is a finite poset, we define its Wiener index as the Wiener index of the graph of its Hasse diagram. In this paper, we find exact expressions for the Wiener indices of the distributive lattices of order ideals in minuscule posets. For infinite families of such posets, we also provide results on the asymptotic distribution of the distance between two random order ideals.
DOI : 10.37236/12002
Classification : 05C09, 05C12, 05C92, 92E10, 05A15, 06A07
Mots-clés : Wiener index, minuscule lattice, order ideals in a rectangle, order ideals in a shifted staircase, order ideals in a ``double tailed diamond''

Colin Defant  1   ; Valentin Féray  2   ; Philippe Nadeau  3   ; Nathan Williams  4

1 MIT
2 Institut Elie Cartan de Lorraine, Université de Lorraine
3 Institut Camille Jordan, Université Lyon 1
4 University of California, Santa Barbara 
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     title = {Wiener indices of minuscule lattices},
     journal = {The electronic journal of combinatorics},
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Colin Defant; Valentin Féray; Philippe Nadeau; Nathan Williams. Wiener indices of minuscule lattices. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/12002

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