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## Synopsis

• Usage:
tLastMon(u,gap,t)
• Inputs:
• u, a t-spread monomial of a polynomial ring
• gap, a positive integer representing the difference between the degrees
• t, a positive integer that idenfies the t-spread contest
• Optional inputs:
• MaxInd => ..., default value -1, optional integer argument for tLastMon
• Outputs:
• , the smallest t-spread monomial of the Borel shadow of u, with respect to lexcografic order

## Description

the function tLastMon(u,gap,t) gives the smallest t-spread monomials of the Borel shadow iterated gaptimes of u, that is, the smallest monomial of $B_\texttt{t}\{\texttt{u}\}$, with respect to $>_\mathrm{slex}.$
If MaxInd is greater than -1 the function tLastMon(u,gap,t,MaxInd=>m) gives the smallest t-spread monomial for which the maximum of the support is m
The Borel shadow of a t-spread monomial u, is defined as the shadow of the strongly stable set generated by u. To work in a t-spread contest, the Borel shadow of u is the t-shadow of $B_\texttt{t}\{u\}$.

Examples:

 i1 : S=QQ[x_1..x_16] o1 = S o1 : PolynomialRing i2 : tLastMon(x_2*x_6*x_10*x_13,1,3) o2 = x x x x x 2 6 10 13 16 o2 : S i3 : tLastMon(x_2*x_6*x_10*x_13,1,3,MaxInd=>14) o3 = x x x x x 2 5 8 11 14 o3 : S